ENGR142 PHYS 115 Geometrical Optics and Lenses

Transcription

1 ENGR142 PHYS 115 Geometrical Optics and Lenses Part A: Rays of Light Part B: Lenses: Objects, Images, Aberration References Pre-lab reading Serway and Jewett, Chapters 35 and 36. Introduction Optics play a central role in our technology and in many areas of science research. Here a laser beam makes its way around an optics system in the Raman Spectroscopy Laboratory at Victoria University. Note the ray-like behaviour of the laser beam. A complex and powerful tool, Raman Spectroscopy is used to study materials used in nanotechnology applications, physics, biochemistry, and material sciences. You can learn more about Raman Spectroscopy and the work in the Victoria University Lab from the following website: Part A: Rays of Light Introduction In the ray model of light we think of rays that travel in a straight line through space, but are reflected from surfaces and sometimes bent as they cross a boundary from one material to another. You might picture laser beams when you imagine rays, Today we will use our optics kits: they use a traditional filament light bulb as a light source. Analysis of uncertainties is important in many of the lab exercises we do in Physics 115, but we will not use uncertainties in the geometrical optics and lens labs. Geometrical Optics: Page 1

2 Part 1 The Law of Refraction The direction of light propagation often changes abruptly as light crosses a boundary between two different media (different materials), such as between air and acrylic, or between glass and n1 n2 water. The change of direction is called refraction and is described quantitatively by the Law of Refraction, also known as Snell's Law: n 1 sin 1 n2 sin 2 Where n 1 and n 2, called indexes of refraction, are properties of the two media. For water n = 1.33 while n varies for different types of glass but might be about 1.5 typically. The angles are measured from the line perpendicular to the surface (called the normal) as indicated by the dotted line in the diagram above. We will now test this law, and also measure the index of refraction for acrylic. Set up the optics bench as shown below. With the slit plate vertical, add the slit mask (see below) on the opposite side of the component holder, so a single ray of light passes directly through the centre of the ray table along the normal line as shown below. Left: Slit mask Right: Slit plate Component line Ray along normal line of ray table is white light (Shown as a red line here.) Light Source Carefully align the flat surface of the cylindrical lens with the line labelled "Component" and with the centre of the flat surface on the centre of the ray table as shown above. If the lens is properly aligned the radial lines extending from the centre of the ray table will be perpendicular to the circular surface of the lens. This needs to be done carefully to get good results. Geometrical Optics: Page 2

3 90 Angle of Incidence 0 0 Angle of Refraction 90 Q1A. Adjust the angle of incidence to. Look carefully at a ray passing from air into the lens and back out through the curved surface. You may need to shield the apparatus from light to see the ray inside the lens. Is the ray bent when it passes through the air to the acrylic at the flat boundary? How about when it passes back into air through the curved boundary? Why are the answers different? Sketch the path of the ray through the lens in your logbook and explain this in terms of Snell s Law. Use measurements of the incident and refracted rays to make an estimate of the refractive index of the material. If time permitted we would collect data at a range of angles and plot sin 1 versus sin 2, obtaining n from the gradient, but time does not permit. Part 2 Reversibility Put arrow labels on your ray table showing the incoming and outgoing rays as indicated below. 90 Stick-on arrows Angle of Incidence 0 0 Angle of Refraction 90 Q2A. Now turn the table until the incident ray enters along the path that was previously followed by the refracted ray. Record the new incident and refracted angles and discuss your results. Q2B. Your results are an example of a general principle of ray optics called light ray reversibility: If light can follow a particular path through an optical system it can also follow the reverse path. Your instructor will show you a more complex system of cylindrical lenses and mirrors in which a light ray can reverse its path. Sketch the path of the rays through the system in your logbook. Geometrical Optics: Page 3

4 Part 3 One-way mirrors Q3A You have seen one-way security mirrors in stores. Is a mirror that lets light pass in one direction but not the other consistent with reversibility of light rays? Your demonstrator will show you how these devices work. Sketch the apparatus and explain the operation of one-way mirrors in your logbook. Part 4 Image Formation with Cylindrical Lenses You may have used spherical lenses to make images in a college laboratory. Moreover, you are used to seeing images formed by such lenses as they are used in projectors, eye glasses, and lots of other places. We will now study image formation using cylindrical lenses, but the ideas we develop also apply to spherical lenses such as the ones we will use in the second part of this experiment. An ideal converging lens will bend parallel rays so that they all intersect the optical axes at the same point on the other side of the lens. The diagram below shows an idealized cylindrical lens doing this. The focal point of a converging cylindrical lens. Optical axis Focal Point Locating the Focal Point Remove the slit mask but leave the slit plate in place. We can make nearly parallel rays using the parallel ray lens. Remove your cylindrical lens from the table and move the parallel ray lens away from and toward the light source to obtain parallel rays on the ray table as illustrated below. Replace and adjust your cylindrical lens so its flat surface is perpendicular to the incident rays and the central ray passes through the lens unbent. Q4A Sketch the results in your logbook. Does it really look like the idealized diagram above, or is there a focal blob instead of a focal point? Geometrical Optics: Page 4

5 Q4B Use a pencil as below to block one ray at a time and observe whether there are particular rays that intersect the optical axis further from the others. You should see that far off axis rays contribute more to the smearing of the focal point and blurring of images. Cylindrical aberration is the distortion of the image caused by imperfect focusing of the refracted rays. If the focal point is a blob then any image will be blurred. Spherical lenses have similar spherical aberrations due to imperfect focusing of rays. Our lens equations and ray diagrams generally ignore this effect but it can be important. You can think of cylindrical and spherical aberrations as lens misbehaviour due to their shapes. If time permits (check with your demonstrator to see whether you have time): Q4C Work alone to make a prediction: We will now consider the reverse process. If we place the vertical filament (essentially a vertical line) at the focal point of the lens, what path should the rays follow? Hint: think about reversibility. Q4D Compare with your lab partners and come to a consensus. Q4E Test this. Note that the filament is about 2 cm from the edge of the light housing. Was your prediction at least approximately correct? Does this work exactly? Perhaps tweak the lens position to try to get the expected result. Again, a focal blob means a distorted image, but the filament is also not exactly a vertical line. It has some horizontal size as well. Part 5 Total Internal Reflection Q5A With rays refracting from plastic to air, use Snell s Law to predict the refracted angle for an incident angle of You should find the mathematics lead to an error. If not, ask for help. Explain where the error arises in mathematical terms. Use the n you found for plastic earlier Q5B. It is certainly possible to set up an experiment with an incident angle of. Do this and describe the results. Q5C Is it possible that light striking an interface between two transparent media cannot pass through the interface? Explain. Q5D. Now adjust the incident angle from 0 to nearly 90. How do the intensities of the reflected and refracted rays vary with the angle of incidence? Geometrical Optics: Page 5

6 Consider again Snell s Law n1 sin 1 n2 sin 2. The largest the outgoing angle 2 could be is 90. The incident angle which causes 2 to reach 90 is called the critical angle. An incident angle larger than c will not allow refraction. All of the light is reflected back into the higher n medium in which the ray started. This is called total internal reflection. If light starts in glass with refractive index 1.6 and is trying to cross a boundary into oil with refractive index 1.2, the critical angle can be determined as follows: c 90 deg n 1 sin 1 n2 sin 1.6sin c 1.2sin c 2 Q5E Calculate the critical angle for your acrylic material using the refractive index you found earlier. Test your predicted critical angle. Does it agree with experiment? Your demonstrator may show you some total internal reflection demonstrations.. Part 6 Colours (ask your demonstrator whether there is enough time left) Arrange the equipment so a single light ray is incident on the curved surface of the cylindrical lens as indicated below and put the screen back. Set the Ray Table so the angle of incidence of the ray striking the flat surface of the lens (from inside the lens) is zero. Adjust the ray table component holder so the refracted ray is visible on the Viewing Screen. Slowly increase the angle of incidence. As you do, watch the refracted ray on the Viewing Screen. You should notice colour separation in the refracted ray, particularly as you approach the critical angle. Dispersion We have treated the refractive index as a constant so far. But for most materials the refractive index depends upon the wavelength (colour) of the light. Snell s Law works, but n is a function of. This dependence of n on is called dispersion and provides a very important practical way to split light up into its component wavelengths. In particular, a prism separates colours not because of its shape. The shape enhances the effect, but it is the dependence of n on colour that is the root cause of the colour separation by a prism. Geometrical Optics: Page 6

7 Part B: Lenses: Objects, Images, Aberration Part 7 A Real Image In this part of the experiment your demonstrator will take the entire class through a series of exercises with lenses. Follow along and ask immediately if you are stuck on something. Recall the focal point of a converging (convex) spherical lens is the spot on the optical axis where parallel rays converge. We will now consider light rays from a point on an object we wish to make an image of. Our objects will generally be an illuminated arrow or the filament of a light bulb. Q7A Sketch the following diagram in your logbook or use the separate sketches provided in the lab and staple/paste them into your logbook. Following your demonstrator s lead, sketch the three principal rays on the diagram and describe each in a few words. Object f Centre of lens from which distances are measured f Optical Axis The lens equation Q7B. Following your demonstrator s lead, use the lens equation to predict the location and size of an image if a 1 cm tall object is placed 0 mm to the left of a 75 mm lens. Testing your prediction Set up the apparatus with a 75 mm converging lens and an object distance of 0 mm. We will use the arrow and circle pattern as an object. You can measure the size of the object and image as the diameter of the circle. Q7C. Put a screen at the image location you predicted. Is the image focused? Adjust the location of the screen until the image is sharp and record the actual image distance and image height in your logbook. Note that a significant source of uncertainty arises from inaccuracies in the focal lengths of the lenses. If the actual image location or size disagrees with your prediction by more than % ask for help. Geometrical Optics: Page 7

8 Q7D. Is the image real or virtual? Explain. Is the image upright or inverted? Explain. Part 8 A Virtual Image Q8A If we place the object inside the focal point we get a quite different result. Sketch the following diagram in your logbook. Following your demonstrator s lead, sketch the three principal rays on the diagram and describe each in a few words. The lens equation Q8B. Following your demonstrator s lead, use the lens equation to predict the location of the image if an object is placed mm to the left of a 75 mm lens. Testing your prediction Set up the apparatus with a 75 mm converging lens and an object distance of mm. Q8C Can you put a screen at the image location you predicted and see an image on it? Your demonstrator will show you how to use the method of parallax to find the approximate location of the image. Does the image location agree at least roughly with the prediction? Q8D. Is the image real or virtual? Explain. Is the image upright or inverted? Explain. Part 9 A Different Lens Recall that focal point for diverging or concave lens is the point from which rays appear to emerge. An image from a diverging lens Q9A. Following along with your demonstrator, sketch a ray diagram showing the location of the image formed by the diverging lens. Geometrical Optics: Page 8

9 The lens equation Q9B Following your demonstrator s lead, use the lens equation to predict the location and size of an image if a 1 cm tall object is placed 0 mm to the left of a -1 mm lens. Testing your prediction Set up the apparatus with a -1 mm converging lens and an object distance of 0 mm. Q9C Use the method of parallax to find the approximate location of the image. Does the image location agree at least roughly with the prediction? Q9D Is the image real or virtual? Explain. Is the image upright or inverted? Explain. Does the size agree roughly with your prediction? Part A Second Lens What happens if we have two lenses? The image formed by the first lens becomes the object for the second lens. QA Following your demonstrator s lead, predict the location of an image formed when a converging lens (1 mm) is placed to the right of the diverging lens. 0 mm QB Test your prediction. Was the prediction correct? QC Following your instructor s lead, explain the observed size of the final image. QD. Following your instructor s lead, make a virtual object and explain what that means. Geometrical Optics: Page 9

10 Part 11 Supplemental Questions Q11A You can trap light in glass due to total internal reflection. Could you trap light in an air bubble inside glass? Explain. Q11B What does the term dispersion mean? If you want to make a prism to separate colours, would you want a material that has a lot of dispersion or little dispersion? If you made a triangular prism out of a material that has no dispersion, would it separate colours? Q11C Dispersion in lens materials results in separation of colours. You may have seen the artificial rainbow edges of small objects under a microscope. Short-sighted people with strong glasses may see rainbow edges on objects they view through the thicker part of their lenses. These are collectively known as chromatic aberrations or colour misbehaviour of lenses. If you are making a lens for a microscope do you want a material that has a lot of dispersion or little dispersion? Q11D Recall the diagram below. Imagine the rays are white light. We have learned two reasons why this diagram is only approximately correct. What are they? Explain briefly. The focal point of a converging cylindrical lens. Optical axis Focal Point Q11E A 2 cm tall object is placed cm to the left of a 0 cm lens. Use the lens equation to find the location and size of the image. Is it upright or inverted? Is it real or virtual? Q11F. A second lens with a focal length of -0 cm is placed cm to the right of the lens in problem Q11G Find the location and size of the final image. Is it real or virtual? Upright or inverted compared to the original object? Q11H Consider a point object (no height) placed on the optical axis at the focal point on the left side of a converging lens. Is there an image? Sketch a ray diagram. Does your diagram look familiar? Geometrical Optics: Page