Optics Learning Goals

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1 I am able to: Optics Learning Goals 1. Light a) Describe how light travels and what light is. b) Explain what an electromagnetic wave is. c) Draw an electromagnetic wave and describe the peak, trough and wavelength of a wave. d) Identify the portion of the electromagnetic spectrum that we can see. e) Describe the order of waves that make up the electromagnetic spectrum. f) Describe frequency and wavelength and how they are used to organize the electromagnetic spectrum. g) Describe the order of colours that make up the visible spectrum. 2. Production of Light a) Explain the terminology used to describe the production of light; specifically incandescence, electric discharge, phosphorescence, fluorescence, chemiluminescence, bioluminescence, triboluminescence b) Describe the difference between luminous and non-luminous objects and give a definition. c) Describe the behavior of light when it is reflected, absorbed, transmitted, refracted, diffracted. d) Describe the difference between transparent, translucent and opaque and be able to draw a picture to describe them. 3. How light travels a) Draw a diagram which describes how images are seen in a pinhole camera. b) Explain how a pinhole camera is similar to a human eye. c) Define and draw a diagram for the following terms: incident ray, angle of incidence, reflected ray, angle of reflection, normal, reflective surface, 4. Law of Reflection a) State the law of reflection. b) Relate the law of reflection to specular and diffuse reflection with diagrams. 5. Plane Mirrors a) Describe what a plane mirror is and what happens when light hits a mirror. b) List the characteristics of images in plane mirrors. c) Describe how to identify a virtual image. d) Draw a diagram which describes how light rays travel from an object to the eye to allow you to see an image in a plane mirror. e) Define lateral inversion. f) Describe what the acronym SALT stands for and how to determine each property. 6. Concave Mirrors a) Draw a concave mirror diagram to scale and label the principal axis, focal point, vertex and the centre of curvature b) Describe what the focal point is and how light has to hit the mirror to go through the focal point. c) Draw the four rays that can be used to identify the location of the image and briefly describe how they occur. d) Locate the location of an image from the description of an object and the concave mirror. e) Give a practical application of concave mirrors. 7. Convex Mirrors a) Draw a convex mirror diagram to scale and label the principal axis, focal point, the vertex and centre of curvature. b) Describe what the focal point is and how light has to hit the mirror to go through the focal point. c) Draw the four rays that can be used to identify the location of the image and briefly describe how they occur. d) Locate the location of an image from the description of an object and the convex mirror. e) Give a practical application of convex mirrors. 1

2 8. Converging Lens a) State the difference between a mirror and a lens b) Draw a converging lens diagram to scale and label the principal axis, optical centre, optical axis, primary focal point and secondary focal point. c) Describe how light has to hit the lens to go through the primary and secondary focal point. d) Draw the three rays that can be used to identify the location of the image and briefly describe how they occur. e) Briefly describe the SALT for the following cases: beyond 2F, at 2F, between F and 2F, at F and in front of F. 9. Diverging Lens a) Draw a diverging lens diagram to scale and label the principal axis, optical centre, optical axis, primary focal point and secondary focal point. b) Describe how light has to hit the lens to go through the primary and secondary focal point. c) Draw the three rays that can be used to identify the location of the image and briefly describe how they occur. d) Briefly describe the SALT for the following cases: beyond 2F, at 2F, between F and 2F, at F and in front of F. 10. Refraction a) Define refraction. b) Draw a labeled diagram with the angle of incidence, incident ray, refracted ray and angle of refraction. c) Describe what a medium is. d) Describe why refraction occurs e) Describe what happens to light (with respect to the normal) when it travels from a more dense to less dense medium. f) Describe what happens to light (with respect to the normal) when it travels from a less dense to more dense medium. g) Describe what happens when light travels from one medium to another medium along the normal. h) Explain what the index of refraction is and know how to calculate it. i) Describe how index of refraction relates to the angles of incidence and angle of refraction. j) Describe how refraction relates to: apparent depth, a bent spoon, a mirage, the flattened sun and a rainbow. 11. Total Internal Reflection a) Describe what total internal reflection is. b) State the conditions for total internal reflection c) To describe, using diagrams, what happens to the refracted/reflected ray as the angle of incidence increases. d) Explain what happens at the critical angle. e) Use Snell s law to determine the critical angle when given the index of refraction for two materials. I am able to read the question, identify given and unknown values and utilize the following formulas to solve a problem. n = sinθi sinθ r c n = v 1 f = d i d o d d i M = = o hi h o 2

3 Light and the Electromagnetic Spectrum What is light? Light is and travels like a A small packet of light energy is called a Light is a visible form of radiation Electromagnetic waves (including light) are made up of electrical energy and magnetic energy Does not require a Other types of electromagnetic waves:, waves, See also Characteristics of a Wave Waves have high points called Waves also have low points called The distance from one crest (or trough) to the next crest (trough) is called a The distance from the centre line to crest or trough is the amplitude Figure 1. Characteristics of a wave. The Electromagnetic Spectrum A graph that shows the various type of electromagnetic radiation (Fig. 3) Arranged by wavelength and frequency Wavelength: distance from peak to or trough to Frequency: the number of peaks that pass a point in a certain Also means per second (measured in Hertz, Hz) The longest waves are the waves The shortest waves are the waves Figure 2. Relationship between wavelength and frequency. NOTE: High frequency & short wavelength = HIGH ENERGY Figure 3. The Electromagnetic Spectrum 3

4 Visible Region of the Electromagnetic Spectrum Light we can Acronym for: Red, Orange, Yellow, Green, Blue, Indigo, & Violet. to Wavelength. Click here to see a prism separating white light Figure 4. The Visible Spectrum Key Facts About Invisible Light All waves shorter than visible light can cause. UV - light - sun burn and skin cancer X-rays can cause cancer (that is why the dentist leaves the room when she X-rays your teeth) rays are the most dangerous they can ALL living things and cause cancer BUT also used to cancer because they cancer cell Try These 1. Draw 3 complete cycles of a wave that has a wavelength of 2.0 cm. 2. Count the number of crests and troughs in the wave you drew from Q#1. Label each crest and trough. 3. What characteristic(s) of a wave is used to arrange the waves in the electromagnetic spectrum? 4. What is the visible spectrum? 5. What does the acronym ROYGBIV stand for? 6. TRUE or FALSE: Ultraviolet light has higher energy than microwaves? 7. TRUE or FALSE: RED light has a shorter wavelength than BLUE light? 8. Although gamma rays are very dangerous, they have a very important use. What are gamma rays used for? Homework Question For each type of wave listed in the previous slides (e.g. radio, microwave, etc ) summarize 2-3 uses of that type of wave. Use the Internet and your general knowledge to locate the information you need. [Thinking] Type of EM Wave Use/Phenomena 4

5 Class Discussion [Application] NASA: The Electromagnetic Spectrum Go to the NASA: Electromagnetic Spectrum website posted above. Spend approx. 5 minutes reviewing each of the different types of electromagnetic waves: Radio waves, Microwaves, Infrared, Visible Light, Ultraviolet, X-rays, Gamma rays. Choose 1 and identify o its physical characteristics, and o example of something equivalent in size and o one thing it is used for in every day life. Post the answers on the Class Discussion thread called "Useful Radiation". Once you have posted, check some answers of your fellow classmates and comment on at least 2 other posts. Additional Homework Questions Consider the electromagnetic spectrum as you answer these questions. 1. Name the region of the electromagnetic spectrum with the shortest wavelength. 2. Name the region of the electromagnetic spectrum with the lowest frequency. 3. Which region of the electromagnetic spectrum has the highest frequency? 4. Which region of the electromagnetic spectrum has the longest wavelength? 5. Which region of the electromagnetic spectrum will travel with the fastest speed? 6. Which region of the electromagnetic spectrum is the most energetic? 7. Consider the visible light spectrum as you answer these two questions. o a. Which color of the visible light spectrum has the greatest frequency? o b. Which color of the visible light spectrum has the greatest wavelength? 8. Label the following diagram. What is Light? List five properties of light (not a complete list): Explain how light is produced: Define luminous à Define nonluminous à Distinguish between natural and artificial light: 5

6 Types of Light Complete the following table. Type Description of how it works Examples/Uses

7 How Light Interacts With Objects Light Rays When you look at an object, you see it because light travels in a line from the object to your eyes. Scientists use an to trace the path and show the direction that light travels The arrow is called a Reflection Reflection is the process in which light a surface and changes Light rays travel from a, the lamp, and from the paper to your eyes. Absorption is the process in which light energy remains in an object and is converted into. Black print on a page all light and therefore no light reaches the eye. Your brain interprets the of light as black Transmission is the process in which light an object and keeps travelling, allowing you to see the objects on the other side. Clear glass and plastic light White paper transmits light and reflects or absorbs the rest Transparent: Light is transmitted without any change in. o Example: clear glass Translucent: Light can pass but is in many different directions. You cannot see a image on the other side. o Example: waxed paper Opaque: No light therefore all light is either reflected or absorbed. o Example: Wood Refraction Light rays appear to when travelling from one medium to another Examples include: o Refraction through a (Dispersion) o Corrective glasses o Fish appear at a different position in aquarium 7

8 Diffraction Diffraction is: o the apparent of waves around small obstacles and o the out of waves past small openings 8

9 Pinhole Camera Lab 9

10 The Ray Model of Light Light Rays Light travels in a A light ray is a and representing the and straight-line path of light Because the candle to the right is radiating light in all, an number of light rays are coming from the candle Terminology Incident Light à light emitted from a source that an object Image à of an object through the use of light Mirror à any polished surface an image (see below) Reflection à the of light from a surface The ray of light approaching the mirror is the ray The ray of light which leaves the mirror is the ray A line drawn perpendicular to the surface of the mirror at the point of incidence where the ray strikes the mirror, is known a line The angle between the incident ray and the normal is the angle of The angle between the reflected ray and the normal is the angle of Homework Answer the following questions: 1. What did you notice in today s lab about the angle of incidence and angle of reflection? 2. Draw a sketch based on today s lab and label the following: mirror, normal, incident ray, angle of incidence, reflected ray, and angle of reflection. 3. In one sentence, summarize the relationship between the angle of incidence and the angle of reflection. Be sure to use the same vocabulary used in your sketch. 10

11 SNC2D 11

12 Reflection The Law of Reflection When a ray of light reflects off a surface, the angle of is equal to the angle of. This relationship can be described mathematically as: normal θ! = θ!. Smooth vs. Rough Surfaces When light rays reflect off of a smooth surface, they do so in the same pattern as the rays. o This produces a image. When light rays reflect off of an irregular or dull surface, the pattern of reflected rays is than the pattern of incident rays. o This produces a or unclear image. Figure 5. The law of reflection states that the angle of reflection is equal to the angle of incidence. Angles Complete the activities on this website to practice measuring angles with a protractor: Figure 6. Specular versus diffuse reflection. What s that law again? reflection occurs when light is reflected off a smooth shiny surface Because light travels in straight lines; o The angle that light strikes the surface ( ) is the same as the angle that light leaves the surface ( ). Terminology : light which travels towards the mirror : light which is reflected by (bounces off) the mirror : imaginary line drawn at 90 degrees to the mirror surface : angle between the incident ray and normal : angle between the reflected ray and normal Diagram Draw a diagram to explain the law of reflection in the space below. 12

13 Law of Reflection 1. The angle of reflection the angle of incidence. 2. The incident ray, reflected ray and normal all lie in the same. Real or Virtual Image? In plane mirror reflection, a image is formed. A image is an image formed by rays that do not actually pass through the location of the image. Image Characteristics In optics, we will describe the characteristics of an image using the acronym L.O.S.T. L - O - (upright or inverted) S - (magnified, reduced, same size) T - (real or virtual) In the table below, write a summary of the image characteristics for a plane mirror. Figure 7. Virtual image produced by a plane mirror. L O S T Figure 8. Image characteristics for a plane mirror. Homework Complete any parts of the Multiple Images lab not finished during class and make sure you fill out the table above. 13

14 STUDENT HANDOUT: Multiple Reflections What You Need 1 set of hinged mirrors 1 copy of The Pirate Handout 1 protractor What To Do 1. Open the hinged mirror and look into it. Slowly change the angle and observe the number of reflections of yourself that you see. If you want to see more reflections, do you make the angle between the mirrors larger or smaller? 2. Place the large R on the table. Open the mirror and place it on the R as shown in the picture at right. Adjust the angle between the mirrors until you see exactly one complete reflection of the R in each mirror. (You will see three R s the original plus two reflections.) Use your protractor to measure the angle between the mirrors and record it in the data table on the next page. In the last column, sketch the pattern you see similar to the sketch below. 3. Move the mirrors until you see three complete reflections of the R in the mirrors. Measure the angle of the mirrors and record the angle in the data table below. In the last column, sketch the pattern you see. Be sure to pay attention to which images of the R are reversed and which are not. 4. Repeat moving the mirrors, increasing the number of reflected R s by one each time, until you see 7 reflections. 5. Create a graph of the number of reflections (y-axis) versus mirror angle (x-axis). Describe the shape of the graph in words. THIS PAGE MAY BE PHOTOCOPIED FOR CLASSROOM OR WORKSHOP USE 32 Copyright 2005 by The International Society for Optical Engineering (SPIE), The Optical Society of America (OSA), and The Association of Universities for Research in Astronomy, Inc. (AURA). All rights reserved. 14

15 6. By looking at your data and at the graph, see if you can predict the angle between the mirrors when you would see eight reflections. Predict the angle for nine reflections. 7. Can you come up with a formula that relates the number of reflections you see to the angle between the mirrors? THIS PAGE MAY BE PHOTOCOPIED FOR CLASSROOM OR WORKSHOP USE 33 Copyright 2005 by The International Society for Optical Engineering (SPIE), The Optical Society of America (OSA), and The Association of Universities for Research in Astronomy, Inc. (AURA). All rights reserved. 15

16 DATA TABLE Number of Reflections Angle Between Mirrors Sketch THIS PAGE MAY BE PHOTOCOPIED FOR CLASSROOM OR WORKSHOP USE 34 Copyright 2005 by The International Society for Optical Engineering (SPIE), The Optical Society of America (OSA), and The Association of Universities for Research in Astronomy, Inc. (AURA). All rights reserved. 16

17 Properties of Plane Mirrors Image Formation in Plane Mirrors An eye catches rays from mirror. Observer has a sensation that image is the mirror. There is nothing behind the mirror. There is no light going to or coming from behind the mirror. Light only to be coming from the image. This image is, or a image. Properties of Images Formed by Plane Mirrors Location - Image is at the same distance from mirror as the object (d i /d o = 1) Orientation - The image is but laterally (Left / Right) Size - The image has the as the object (h i /h o = 1) Type - Plane mirrors form images (no real light is there) Image Formation in Plane Mirrors Point Objects Both green and red rays, coming out of point A, are reflected such as θ! = θ!. Their meet at A behind the mirror. The image is formed at the point where the extensions of the reflected rays. Due to the symmetry of the diagram about the mirror surface, d! = d! and AA mirror See this link A d o d i A A d o d i A No matter where the observer is, due to the symmetry on the diagram to the left, all the extensions of reflected rays meet at the same which is: the object object point, A, the mirror on the line passing through at the same distance from the mirror as the THEREFORE: rays are enough to locate the image 17

18 Drawing Ray Diagrams in Plane Mirrors Draw an object (use an arrow) that is 6 cm tall. Draw this object 10 cm from a plane mirror. Locate extreme points on the object. For EACH of the extreme points: 1. Draw a light ray perpendicular to the mirrored surface. This light ray reflects back on itself (Represent this using arrowheads). Extend this reflected ray behind the mirror. 2. Draw a second light ray from the point to anywhere on the mirror. Draw in a normal line where the incident ray meets the mirror. Measure the angle of incidence. Draw in the reflected ray, where the angle of incidence equals the angle of reflection. Extend the reflected ray behind the mirror. 3. Where the two reflected rays meet that originated from the same point on the object is where the image of that point will be formed. 4. Connect the image by using the two extreme points you found. Example: 18

19 S EEING I MAGES IN PLANE (FLAT) MIRRORS 1. Show how the Eye/Brain sees the Image of the Object in the diagram below 2. Show how the Eye/Brain sees the Image of the Object in the diagrams below 19

20 3. Which Eye/ Brains can see the Object? 4. Which Eye/ Brains can see the Image? Full Body Mirror 5. How big does a Mirror have to be in order to see yourself Head to Toe? (Hint You see your image) 6. If you can just read the Middle line of an Eye Chart taped onto a Mirror. Which line of the same sized Eye Chart could you read when viewed in a Mirror? Would it be, a) one Line up (2X s Larger) b) the same line c) one line down (Smaller by half) 20

21 SNC2D0 Plane Mirror Practice Questions 1. An object 4 cm high is located 15 cm in front of a plane mirror. List the four image properties of this image. L- O- S T - 2. A student stands 3 m in front of a plane mirror on his head a) What is attitude of the image? b) How far behind the mirror is the image? c) How far from his image is he? d) If he moves ahead 1m how far will he be from his image? 3. A student approaches a plane mirror at a speed of 2 m/s. a) at what speed does her image approaches the mirror? b) at what speed does she approach her image? 4. What is the real time if the time on a clock (with no numbers) appears to read the following times when viewed in a plane mirror? a) 8:00 b) 7:30 c) 6:00 d) 3:00 21

22 Ray Diagrams and Plane Mirrors 22

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25 Name: Concave Mirrors Lab Terminology: vertex Concave Mirror Principal axis Part A: Concave Mirrors 1. Set-up the ray box for 5 rays and adjust until rays are parallel. 2. On a blank sheet of paper, draw a line for the principal axis of the mirror. 3. Place the mirror on the principal axis and mark its position on the paper. 4. Use the ray box to send 5 parallel incident rays on to the mirror. Place the centre ray on the principal axis. The position where the 5 rays are focussed into a point is called the focus or focal point. 5. The distance from the vertex to focus of a mirror is called the focal length. 6. Measure the focal length of your mirror. Focal length (f) = 7. Make a neatly labelled diagram showing the concave mirror (with reflective surface), its principal axis, the vertex, focal point, focal length, incident rays and reflected rays Part B: Four principal rays for a Concave mirror 1. On a blank sheet of paper, draw a line to represent the principal axis. Place a concave mirror on the axis and mark its position. 2. Use a ray box to locate the focal point for the mirror. Mark the position on your diagram. 3. The centre of curvature for a mirror is located on the principal axis at a distance of twice the focal length from the vertex in front of the mirror. (i.e. C = 2 x f) Mark the centre of curvature for your mirror on your diagram. 25

26 4. In each of the following mark the path of the reflected ray for each of the given incident rays (use the plate that only has one slit) a) incident ray parallel to principal axis b) incident ray passing through the focus Incident rays parallel to the principal axis are reflected in such a way that the reflected rays Incident rays passing through the focus are reflected in such a way that the reflected rays c) incident ray passing through the d) incident ray striking the vertex centre of curvature Incident rays passing through the Centre of Curvature are reflected in such a way that the reflected rays Incident rays striking the vertex of the mirror are reflected in such a way that the reflected rays 26

27 Concave Mirrors Spherical Mirrors A spherical mirror has the shape of a section of a sphere. If the outside is mirrored, it is. If the inside is mirrored, it is. (Fig. 1) Concave & Convex Mirrors For a concave mirror, both the focal point (F) and the centre of curvature (C) are in front of the mirror. For a convex mirror, both the focal point (F) and the centre of curvature (C) are behind the mirror. Incoming light ray Figure 1. Concave and convex mirrors. Figure 2. Concave mirror. Incoming light ray Figure 3. Convex mirror. Focal Length Concave Mirrors Parallel rays hitting a spherical mirror come together (intersect) at the Focal point, F, is the mirror The distance from the focal point to the vertex of the mirror is the, f Terminology 27

28 Constructing Ray Diagrams 1. P ray: A light ray parallel to the principal axis is reflected through the. This is how the focus is defined. 2. C ray: A light ray through the centre of curvature is reflected back. This rule makes sense because any line through the centre of curvature is a radius of the circle formed by the mirror. A radius is always at 90 to the mirror. A ray along the normal has an angle of incidence of 0. This means that the angle of reflection is also 0. The reflected ray will return back on the same path. 3. F ray: A ray through F will reflect to the principal axis. This rule uses the fact that the angle of incidence is always to the angle of reflection. Even if you switch the incident and reflected rays, the light will still follow the same path; only the direction will change. This principle is called the of light. 4. V ray: A ray aimed at the vertex will follow the law of. Because the principal axis is perpendicular to the surface of the mirror, the angle of incidence can be easily measured (not widely used as it requires the use of a protractor). Summary: Incident Ray Parallel to principal axis Reflected Ray Through the focal point Through C Through vertex θ How do we see an image? A point object emits (or reflects) light in all All the rays reflected by the mirror meet at one Eye detects the light that hits the Ray Diagrams for a Point Source No need to draw that many rays to find the image O Draw any two out of four rays originating from the point object Image is located at the intersection of their rays Any other reflected rays will at this point as well O Ray Diagrams for a Non-Point Source For non-point objects, use points (as in plane mirrors) IMPORTANT - Any point on axis will form image on. O O 28

29 Concave Mirror Image Properties Summary Object location (d o ) Location Orientation Size Type Beyond C At C Between F and C At F Between F and the Mirror Scale Ray Diagrams A pencil 15 cm high is located 60 cm in front of a concave mirror with a focal length of 20 cm. Construct a scale diagram to correctly determine the location of the image and its height. [Thinking] (indicate the scale used) Ray Diagram Practice 1. Mark and label the focal point and the centre of curvature of the mirror in this diagram. 2. What is the orientation of the image when an object is located between a concave mirror and its focal point? 3. What is the orientation of the image when an object is located between the focal point and the centre of curvature of a concave mirror? 4. Is it possible for the image to be upright when an object is 30 cm away from a concave mirror with a focal length of 25 cm? Explain your reasoning. 5. A concave mirror has a focal length of 5 cm. An object 2 cm high is 11 cm from the mirror. Draw a scale ray diagram. Measure the image height and image distance. Homework: Complete the Concave Ray Diagram sheet, along with the above question 29

30 Convex Mirrors For a convex mirror, both F and C are behind the mirror Because of this, the mirror has a negative focal length Figure 9. A convex mirror has F and C behind the mirror, and a negative focal length. Constructing Ray Diagrams When constructing ray diagrams with convex mirrors, use the same principle rays as for concave mirrors. The principle rays are shown below. 5. P ray: A light ray parallel to the principal axis is reflected as if it had come through the. 6. C ray: A light ray aimed at the centre of curvature is reflected back. 7. F ray: A ray aimed at the focus (F) is reflected to the principal axis. Figure 10. Principle rays for a convex mirror. *Always remember that when locating an image, ALL RAYS ORIGINATE FROM THE! Convex Mirrors Focal Point For convex mirrors: Parallel rays hitting a spherical mirror to come together (intersect) at the focal point Focal point, F, is mirror 2F = C Note: use dotted lines to represent imaginary light rays Image Formation Using Ray Diagrams for a Convex Mirror Figure 4. Projections of reflected P, C, and F rays cross at the location of the image. 30

31 Image Properties Location Orientation Size Type *Note: For a convex mirror, image properties are the regardless of object location. See animation Figure 5. Locating an image produced by a convex mirror. For a convex mirror, rays from the object will (i.e. spread out) upon being reflected, thereby appearing to originate the mirror. The image is located where the (dashed lines) of the three rays cross (intersect). Use dashed lines to extend rays behind mirror. The size of the image can be determined if you draw your diagram to. LOST for Concave vs. Convex Mirrors Concave Mirror Location Orientation Size Type *Image properties depend on object location Convex Mirror Location Orientation Size Type *Image properties are the same regardless of object location Try One! An object 5 cm high is placed 10cm in front of a convex mirror with a focal length of 20cm. Using a scale ray diagram identify the characteristics of the image. Homework: - Complete the above practice question if not done already - Convex mirrors ray diagrams sheet complete all diagrams and LOST for each - Concave mirrors problem set due Nov. 1 31

32 Object Position Ray diagram Image properties L Beyond C O S T L At C O S T L Between F and C O S T L At F O S T L Between F and Mirror O S T 32

33 Object Position Ray diagram Image properties L Beyond C O S F C T L At C O S T L Between F and C O S T L At F O S T L Between F and Mirror O S T 33

34 Concave Mirrors Ray Diagrams Problem Set Each diagram must have: principal axis and a mirror (use a protractor to trace a curved surface). Reflective side of the mirror must be made clear (shading) an object represented as an up-right arrow with an appropriate (to scale) height a scaled ray diagram showing two principal rays coming out of the object s extreme point. the image at the intersection of the reflected rays Using scale, identify image properties and answer the questions. 1. A nail 5 cm high is in front of a concave mirror 5 cm beyond the focal point. If the focal length of the mirror is 15 cm, what is the size of the image formed? 2. A candle 7 cm high is placed 15cm away from the vertex of the concave mirror with the focal length 25 cm. a. What is the location of the image? b. What is the size of the image? 3. A person eating cereal happens to peer into his spoon. If his face is 18 cm from the spoon and is 21cm long. The focal length of the spoon is 3 cm: a. how far from the spoon is the image? b. measure the size of the image An object 10cm high is placed 15cm in front of a concave mirror with a focal length of 5 cm. Identify all the characteristics of the image. 34

35 Converging (Convex) and Diverging (Concave) Lenses Terminology: Part A: Convex Lenses 8. Set-up the ray box for 5 rays and adjust until rays are parallel. 9. On a blank sheet of paper, draw a line for the principle axis of the lens and a line for the optic axis (see diagram above). USE A RULER! 10. Place the converging lens on the principle axis and mark its position on the paper. 11. Use the ray box to send 5 incident rays through the lens. Place the centre ray on the principle axis. 12. Define: Focal point Focal length 13. Measure the focal length of your lens using a ruler. Focal length (f) = 14. Why does any lens have two focal points? 15. Make a neatly labelled diagram, using a ruler, of the converging lens showing the principal axis, the vertex, BOTH focal points, focal length, incident rays and refracted rays. 35

36 Part B: Principal Rays for a Convex Lens 5. Using the other side of your paper, draw a line to represent the principle axis. Place a converging lens on the axis and mark the position of it. (hint: trace the same lines as on the other side of the page if possible) 6. Use a ray box to indicate the position of both focal points for the lens. Mark these positions on your diagram. 7. Set up your ray box for a single ray and use the diagrams below to direct your rays. 8. Complete each of the following diagrams by marking the path of the refracted ray for the given incident rays and complete the summaries: Incident rays parallel to the principle axis are refracted in such a way that the refracted rays Incident rays passing through the vertex are refracted in such a way that the refracted rays Incident rays passing through F are refracted in such a way that the refracted rays Part C: Diverging (Concave) Lenses 1. Repeat steps 1 to 4 above using a diverging lens. 2. How do you locate the focal point for this lens? Concave Lens 3. Measure the focal length of your lens. Focal length = 4. Make a neatly labelled diagram of the convex lens showing the principal axis, the vertex, focal point, focal length, incident rays and refracted rays. 36

37 Converging and Diverging Lenses What are lenses? Lenses are used to light and form. There are a variety of possible types We will consider only the ones o the double and the double Converging at the Focal Point For a double convex (i.e. ) lens, the light refracts such that it converges at the focal point. Diverging from the Focal Point A double concave (i.e. ) lens has the refracted rays diverging as if they all come from the focal point. Constructing Ray Diagrams Draw of the principal rays originating from the same on the object and follow these rules: 1. P-Ray is drawn through a point on the object and to the principal axis. o It is refracted through the, F. 2. F-Ray is drawn through a point on the object and through (convex) or towards (concave) the. o it is refracted to the principal axis. 3. V-Ray is drawn through a point on the object and through the. o It goes straight and does NOT change (assuming lens is thin) 37

38 Converging Lenses Converging = The convex lens forms different image types depending on where the object is located with respect to the 5 possible object locations 1. Case 1: The object is located in front of F 2. Case 2: The object is located at 2F 3. Case 3: The object is located beyond 2F 4. Case 4: The object is located between F and 2F 5. Case 5: The object is located at F, the focal point. Please complete handout for CONVEX lenses (front half) (two examples are done for you on the next slides to help get you started) Diverging Lenses Diverging = Complete the ray diagrams for concave/diverging lenses You only need to complete two or three of these if you catch on to the trend, you can stop Summary: Image Characteristics formed by Concave and Convex Lenses Concave Lens (Diverging) Object Location Size Attitude Location Type Arbitrary Convex Lenses (Converging) Object Location Size Attitude Location Type Beyond 2F At 2F Between F and 2F At F In front of F Homework Complete ray diagrams and fill in table above 38

39 Ray Diagrams for Converging Lenses Object Position Ray diagram Image properties L Beyond 2F O S T L At 2F O S T L Between F and 2F O S T L At F O S T L Between F and Lens O S T 39

40 Ray Diagrams for Diverging Lenses Object Position Ray diagram Image properties L Beyond 2F O S T L At 2F O S T L Between F and 2F O S T L At F O S T L Between F and Lens O S T 40

41 Problem Set: Lenses 1. A 16mm high object is viewed with a converging lens of focal length 32 mm. For each object distance listed below: a. draw a scaled ray diagram using all the rules to locate the image of the object b. State the characteristics of each image (LOST) i. d o = 64 mm ii. d o = 52 mm iii. d o = 16 mm 2. Below is a list of optical devices. For each of the following cases, explain what kind of lens must be used and where the lens must be placed relative to the object: a. A copy camera produces an image that is real and the same size b. A slide projector produces an image that is real and larger c. A spotlight produces parallel light; there is no image d. A photographic enlarger produces an image that is real and larger 3. A pencil 15 cm high is placed 45 cm in front of a converging lens with a focal length of 12 cm. Using a scale ray diagram find: a. The distance from the lens to the image [16 cm] b. The distance from the object to the image [61cm] c. The image height [5.3 cm] 4. For the object and distances from Question 1, calculate di using the thin lens equation and calculate your percent error. 5. For the object in Question 3 calculate di and your percent error. 6. An image formed by a diverging lens is only ¼ as far from the lens as the object. Find the distance from the image to the lens if the focal length is 30 cm. [38cm] 7. The sun is 1.49X m from the earth. A converging lens with a focal length of 32cm is used to form an image of the sun. a. How far from the lens is the image formed? [32 cm] b. How might you have guessed this result without even performing the calculation? 8. A tree 11cm from a converging lens forms an image 78cm from the lens. Calculate the focal length of the lens. [73cm] 9. A projector lens has a focal length of 25cm. A 35mm slide is placed 26 cm from the converging lens. a. How far away from the lens must the screen be positioned? [650 cm] b. What is the size of the image formed on the screen? [875 mm] 10. An object is 3 times the distance to a converging lens as its image is. If the focal length of the lens is 25 cm, how far from the lens is the object? [100cm] 41

42 Refraction Lab 42

43 Table of Sin(a) + Text Only Site + Non-Flash Version + Contact Glenn 1 of 2 16/10/2012 9:47 AM 43

44 Refraction What is refraction? The or change in of light as it passes from one substance (medium) to another substance (medium) of differing Why does light bend? Refraction happens because the light slows down in the new material Figure 11. When the wagon travels from pavement to sand, its right front wheel hits the sand first, causing it to slow down. Since the left front wheel is moving faster than the right front wheel, the wagon turns to the right. Rules of Refraction Speed of light changes depending on the through which it is travelling The angle of refraction is the angle between the ray and the normal Light bends toward the normal when the speed of light in the second medium is than the speed of light in the first medium Light bends away from the normal when the speed of light in the second medium is than the speed of light in the first medium Practice In each diagram, draw the "missing" ray in order to appropriately show that the direction of bending is towards or away from the normal. Basic Properties of Refraction When a ray of light enters a medium where its speed decreases, it is bent the normal. When a ray of light enters a medium where its speed increases, it is bent the normal There is no change in if there is no change in the index of. The greater the change in index of refraction, the the change in direction. 44

45 If a ray of light goes from one medium to another along the, it is not refracted, regardless of the index of refraction The Bent Spoon The spoon looks broken in a glass of water The light rays bend as they go from the air into the water in the glass The pattern of the light rays gets distorted due to refraction The Index of Refraction The ratio of the speed of light in a (c) to the speed of light in a (v) is called the index of refraction and is represented by the letter n. n = c v This is a physical property of the substance (like melting and boiling point) c = speed of light in a vacuum (3.00 x 10 8 m/s) v = speed of light in the material Practice What is the index of refraction of a liquid in which the light travels at 2.04 x 10 8 m/s? The Refraction of Light Here are some typical indices of refraction: 45

46 Snell s Law The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant (for the same medium): sin θ! sin θ! = n where θ i is the angle of incidence and θ r is the angle of refraction. We can now write the angle of refraction in terms of the index of refraction: n! sin θ! = n! sin θ! This relationship is known as. Note: the incident ray and the refracted ray are on sides of the normal Practice 1. If light passing from water to glass has an angle of refraction of 32, find the angle of incidence. (n glass = 2.42 and n water = 1.33) 2. Calculate the angle of refraction in the diagram below. n air = 1.00; n water = Calculate the angle of refraction in the diagram below. n air = 1.00; n glass = 1.52 Refraction of Light Problems 1. The speed of light in glass is 2.0 x 10 8 m/s. Calculate the index of refraction for the glass. 2. If light passing from water to glass has an angle of refraction of 25, find the angle of incidence. (n glass = 1.46 and n water = 1.33) 3. The index of refraction for ethanol is Calculate the speed of light in ethanol. 4. The angle of incidence in diamond is 20. What is the angle of refraction in air? 5. The speed of light in leaded glass is 1.66 x 10 8 m/s. That is the index of refraction for this type of glass? 6. The speed of light through a material is 1.24 x 10 8 m/s. What is the material? 7. Light travels from air (n=1.00) into an optical fiber with an index of refraction of If the angle of incidence on the end of the fiber is 22 o, what is the angle of refraction inside the fiber? 8. What is the speed of light through alcohol? 46

47 Phenomena Related to Refraction Summarize the following phenomena using internet research Apparent depth The flattened Sun Mirages The rainbow Homework Refraction problems from above Post to the class discussion for the Snell s Law Lab Curved mirror problem set due Feb 18 Total Internal Reflection When light travels between media, some light is and some is Light bends the normal when it speeds up at the boundary of two media o Angle of refraction is larger than the angle of incidence (Fig. 1) Critical Angle The angle of refraction continues to increase as the angle of increases. Eventually, the angle of refraction will become (Fig. 3) o At this point, the angle of incidence is called the If the angle of incidence is increased the critical angle, the refracted ray will not exit the medium (Fig. 4) o It will back into the medium o This is called Figure 14. Incident ray at less than the critical angle. Click HERE Figure 14. Incident ray at the critical angle. Figure 14. Total internal reflection occurs when the angle of incidence is greater than the critical angle. Conditions for TIR Total internal reflection occurs when 2 conditions are met: o Light is travelling more in the first medium than in the second o The angle of incidence is larger than the critical angle Calculating Critical Angle Use Snell s law to calculate the critical angle for a water -> air boundary. Homework Complete virtual lab Post one TIR application to class discussion 47

48 The Thin Lens Equation Converging/Convex Lenses In convex lenses, o f is o d o is always o d i can be or Diverging/Concave Lenses In concave lenses, o f is o d o is always o d i is The Thin Lens Equation The thin lens equation is: Where f is the, d 0 is the distance from the to the lens, and d i is the distance from the to the lens. To use the thin lens equation, you need to follow this sign convention: o Object distances (d o ) are always o Image distance (d i ): o Are for real image (image is opposite side of lens as object) o Are for virtual images (when the image is on the same side of the lens as object) o The focal length (f) is for converging lenses and for diverging lenses. Sample Problem Calculate d i for the following diagram. 48

49 Calculating Percent Error You can check the accuracy of your drawings by comparing your to your calculations. o Theoretical is the image distance you using the thin lens equation o Experimental is the image distance you on your scale ray diagram o If you get a negative percent just ignore the negative sign. Homework Lenses Problem Set questions 4-11 Snell s Law & Thin Lens review practice sheets theoretical experimental %error = x100% theoretical 49

50 Skills Reference 12 Snell s Law Snell s law relates the indices of refraction of a material to the angles of incidence and reflection. It uses values for the index of refraction to calculate the new angle that a ray will take as a beam of light strikes the interface between two media. If you call the indices of refraction of the two media n 1 and n 2 and call the angle of incidence and the angle of refraction θ 1 and θ 2, then the formula for Snell s law is: n 1 sinθ 1 = n 2 sinθ 2 A table of indices of refraction for selected substances can be found below. Index of Refraction for Selected Substances Substance Index of Refraction Example Problem 12.2 When light passes from air into water at an angle of 50 from the normal, what is the angle of refraction? Identify air as medium 1 and water as medium 2. air water 1.33 Plexiglas 1.49 sapphire 1.77 Given Index of refraction of air = n 1 = 1.00 Index of refraction of water = n 2 = 1.33 Angle of incidence θ 1 = 50 Required Angle of refraction = nθ 2 Analysis and Solution The correct equation is sinθ 2 = Substitute the values and their units, and solve the problem. sinθ 2 = n 1 sinθ 1 n sin(50 ) = ( ) 1.33 = sin ( ) 1.33 = 0.58 Therefore, θ 2 = 35 Paraphrase The angle of refraction is 35. n 1 sinθ 1 n 2 Instant Practice 1. When light passes from air into water at an angle of 40 from the normal, what is the angle of refraction? 2. When light passes from water into sapphire at an angle of 35 from the normal, what is the angle of refraction? 3. When light passes from air into Plexiglas at an angle of 15 from the normal, what is the angle of refraction? 4. When light passes from air into water at an angle of 30 from the normal, what is the angle of refraction? 5. When light passes from water into sapphire at an angle of 45 from the normal, what is the angle of refraction? 6. When light passes from air into Plexiglas at an angle of 20 from the normal, what is the angle of refraction? 550 Skills Reference 12 Optics 50

51 Skills Reference 12 The Thin Lens Equation The thin lens equation relates three qualities about thin lenses: d o distance from lens to object d i distance from lens to image f focal length of the lens. The relationship takes the form of an equation, called the thin lens equation: 1 f 1 = + d o 1 d i Remember that for convex lenses, some distances are taken to be negative. The table below shows these: Images Formed by Convex Lenses Example Problem 12.3 A convex lens of a magnifying glass is held 3.00 cm above a page to magnify the print. If the image produced by the lens is 4.20 cm away and virtual, what is the focal length of the magnifying glass? Given Distance of the object from the lens, d o = 3.00 cm Distance of the virtual image from the lens, d i = 4.20 cm Required Focal length of the lens, f Analysis and Solution The correct equation is f = + Substitute the values and their units, and solve the problem 1 f 1 f 1 1 = ( ) = d o cm d i 1 cm Take the reciprocal of both sides. f = 10.5 cm Paraphrase The focal length is about cm. Lens Type Focal Point Distance to Object Distance to Image Convex positive positive positive or negative depending on object location Instant Practice 1. A powerful magnifying glass produces a real image 5 mm from the convex lens. If the object was placed 35 mm away, what is the focal length of the lens? 2. A concave lens has a focal length of 12 cm. An object placed 8 cm away is virtual, upright, and smaller. What is the distance of the image from the lens? 3. A convex lens with a focal length of 25 mm produces an image 30 mm from the lens. How far from the lens is the object? 4. Determine the focal length of a convex lens that produces a virtual image at a distance of 40 mm, when the object is placed 20 mm away. 5. A convex lens focusses the light from a bacterium that is cm from the lens. If the focal length of the lens is cm, how far from the lens is the image? 6. Where is the object placed if a convex lens with a focal length of cm produces a virtual image 4.00 cm from the lens? 51 Skills Reference 12 Optics 551

52 Lab: Images Produced by Converging Lenses Submission & Evaluation: Each student will submit a formal lab report. The formal lab report rubric for this lab is at the end of this document. The report should be clearly organized and include: Purpose Hypothesis Materials Procedure Observation Table Analysis Discussion/Conclusion Extension Refer to the Nelson Skills Handbook posted on ANGEL, p.601, Purpose: The purpose of this investigation is to determine the relationship between the focal length, the image distance and the object distance of a converging lens. In this lab you will be investigating 5 cases in which the resulting image will differ based upon the location of the object with respect to the lens: Case 1: the object is located beyond 2f Case 2: the object is located at 2f Case 3: the object is located between 2f and the focal point (f) Case 4: the object is located at the focal point (f) Case 5: the object is located in front of the focal point (f) Hypothesis: Make a statement in response to the purpose. It should clearly conjecture an outcome that covers every case and is testable. It should address all the LOST characteristics. It should be in the form As the object moves closer to the lens, the image. Materials: Record a detailed list of all materials you use in this lab. Be specific. For example, instead of saying track you could say 1 m long track. Safety Considerations: Watch when moving equipment that you don t tip the track off the desk or accidentally hit another student. Remember Sign Conventions: Object and image distances are measured from the optical centre of the lens. Object distances are positive if they are on the same side of the lens from which the light is coming; otherwise they are negative. Image distances are positive if they are on the opposite side of the lens from which the light is coming; if on the same side, the image distance is negative. (Image distance is positive for real images and negative for virtual images) Object heights and image heights are positive when measured upward and negative when measured downward from the principal axis 52

53 Procedure: You must come up with the procedure for this lab and record it in your lab report. Remember, procedure steps should be simple, present- tense, actions that another student could complete in order to get your same results. The first couple have been completed for you below. You still need to include them in your lab report. 1. Determine the focal length of your converging lens. Set your ray box to send out a wide beam of light and hold it about a metre away from your lens. Use your screen to locate the point on the opposite side of the lens where the light is focused to a point. Measure the distance between the screen and the lens: f = 2. Turn the lens around and repeat step 1 (to verify your measurement) f = 3. Calculate an average of both f measurements. f avg = 4. Using this average value, calculate the following object distances and record them in the attached table: 2.5f = 2.0f = 1.5f = f = 0.5f = 5. Start adding your own steps here. Observations: Complete the observation table below and perform relevant calculation. Remember sign conventions! Case Object L O S T 1/ d o 1/ d i 1/ d o + 1/f Distance (d i ), (h i), 1/ d i (d o ), cm cm cm 1 2.5f = 2 2.0f = 3 1.5f = 4 f = 5 0.5f = Show sample calculations in your lab report. Analysis: 1. As the object moves closer the lens what regular changes occur: to the size of the image? to the distance of the image? to the attitude of the image? 2. At what object distance was it difficult, if not impossible, to locate a clearly focused image? 53

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