Exam Review: Geometric Optics 1. Know the meaning of the following terms and be able to apply or recognize them: physics transparent convex mirror real image optics translucent refraction virtual image wavelength opaque refractive index magnification amplitude umbra total internal reflection SALT frequency penumbra critical angle angle of incidence non-luminous regular reflection converging lens angle of reflection incandescent diffuse reflection diverging lens angle of refraction luminescent concave mirror optical centre normal 2. Use the conversion factor method to convert between the following units. You must know the conversion factors and show all work. a) 360 nm x 1.0 m = 0.00000036 m or 3.6 x 10 7 m 1.0 x 10 9 nm b) 5.35 m x 1.0 x 10 9 nm = 5350000000 nm or 5.35 x 10 9 nm 1.0 m c) 115 km x 1000 m = 115000 m or 1.15 x 10 5 m 1 km d) 58 m x 1 km = 0.058 km 1000 m 3. What is the speed of light in a vacuum? 3.0 x 10 8 m/s 4. The four laws we have studied related to light: a) The Law of Conservation of Energy: energy can neither be created nor destroyed but it can be converted between different forms. For example, we can convert many different types of energy to light: mechanical energy to light eg. mechanoluminescence (crushing wintogreen candies) nuclear energy to light when small atoms smash together in the sun chemical energy when chemical reactions produce light b) The Law of Reflection: the angle of incidence is equal to the angle of reflection when measured from the normal. This law allows us to predict the location of images in plane and curved mirrors. c) Snell s Law: n 1 sine θ 1 = n 2 sine θ 2 This law can be used to predict the angle of refraction if the indexes of refraction and incident angles are known. It can also be used to determine the index of refraction of an unknown substance (eg. fake diamonds) to identify them.
d) The three Laws of Refraction: when light travels from a less dense to a more dense substance at an angle, it slows down and bends toward the normal. This can be used to explain why light bends when it moves from the air into a prism as shown in the picture to the right. when light travels from a more dense to a less dense substance at an angle, it speeds up and bends away from the normal. This can be used to explain why the light leaving the prism and re-entering the air speeds up and emerges parallel to the first incident ray. It is also used to explain why light bends when it leaves the water and enters the air so objects appear to be closer to the surface of the water than they really are. when light travels from a less dense to a more dense substance and hits the surface exactly along the normal, it slows down but does not bend. This is useful to explain why light that shines down straight into the water does not bend. 5. Be able to label the trough, crest, rest position, wavelength and amplitude on a diagram of a wave. a) What is the importance (significance) of the wavelength of light? Wavelength determines the amount of energy that the electromagnetic radiation has. In the case of visible light, it is the wavelength that determines the colour of the light. rest position b) What is the importance (significance) of the amplitude of light? The amplitude of a wave determines its intensity. In the case of light, amplitude determines the intensity or brightness of the light. c) What is the importance (significance) of the frequency of light? The frequency of light is another indication of its wavelength or energy. The higher the frequency, the shorter the wavelength and the higher the energy. 6. The primary and secondary additive colours: the primary additive colours are red, green and blue the secondary additive colours are magenta, cyan and yellow The primary and secondary subtractive colours: the primary subtractive colours are magenta, cyan and yellow the secondary subtractive colours are red, green and blue 7. According to Subtractive Colour Theory: a) to appear red, an object absorbs blue and green light, and reflects red b) to appear blue, an object absorbs green and red light, and reflects blue c) to appear green, an object absorbs red and blue light, and reflects green
8. What three ways can light be produced by luminous objects? Give an example of each. Nuclear reactions. Nuclear reactions can occur two ways. If two small nuclei smash together, they can fuse to form one large atom and release energy as light. This is what takes place in the sun and stars. A large atom can split apart into two or more smaller atoms and release energy as light. This is what occurs in nuclear reactors and bombs. Incandescence. This is when objects are heated to very high temperatures and then give off energy as light. This takes place in incandescent lightbulbs and the elements of electric stoves and toasters. Luminescence. This is when the electrons in atoms are excited by the addition of energy. The electrons jump away from the nucleus to higher energy levels. Eventually the electrons drop back closer to the nucleus and release their energy as light. Luminescence is classified by the source of the energy used to excite the electrons. For example, magnesium burns and gives off light by chemiluminescence. Phosphorescent objects absorb light from radiant energy and then release it as visible light. 9. Explain what happens in an atom when light is produced by luminescence. When the electrons in an atom are excited by the addition of energy (from a chemical reaction or electricity or other light energy or any other source of energy), the electrons jump further from the nucleus to higher energy levels. Eventually the electrons drop back closer to the nucleus and release their energy as light. 10. For fluorescent and incandescent light bulbs: incandescent light bulbs create light by first becoming very hot. Electricity passes through a tungsten filament, which becomes so hot that it gives off light. Because electricity if first converted to heat, and then to light, these light bulbs are very inefficient. fluorescent light bulbs create light when electricity excites the electrons in atoms of mercury within the bulb. When the electrons drop back to lower energy levels closer to the nucleus, they release ultra violet light. The UV light strikes a phosphor lining inside the bulb which then gives off white light. Fluorescent bulbs are more efficient than incandescent bulbs, but they still involve two energy conversions, so they are not very efficient fluorescent bulbs are more efficient than incandescent bulbs 11. What three things can happen to light when it hits the surface of an object? when light hits a surface, it can be reflected, transmitted or absorbed. If it is transmitted, it may be refracted (bent) depending on the angle of incidence and refractive indexes. 12. What is a shadow? Explain how the following factors affect the characteristics of a shadow: a shadow is a dark area that receives little or no light because the light has been blocked by a translucent or opaque object. a) the size of light source: the larger the light source, the larger and more blurry the shadow because it has a larger penumbra b) the size of the object: the larger the object, the larger the shadow because the object can block more light c) the transparency of object: the more transparent an object, the more light it allows to pass through and the lighter the shadow. Transparent objects can not create shadows, translucent objects create pale shadows (penumbras) and opaque objects create very dark shadows (umbras) d) the location of object: the closer the object is to the light source, the larger the shadow.
13. Draw the images of the objects as they are reflected by the curved mirrors. Describe their SALT characteristics. Include a calculation of the magnification (include the formula). S: larger A: inverted L: in front T: real = 2.1 cm / 1.1 cm = 1.9 x (about) S: larger A: upright L: behind T: virtual = 2.1 cm / 1.1 cm = 1.9 x (about) smaller upright S: A: L: behind T: virtual = 0.4 cm / 1.1 cm = 0.36 x (about) S: smaller A: upright L: behind T: virtual = 0.6 cm / 1.0 cm = 0.6 x (about)
14. Describe two uses of concave mirrors. Describe two uses of convex mirrors. Concave mirrors are used for magnifying, for example for make-up mirrors and for telescopes. Convex mirrors are used to collect light from a large area, for example, side-view mirrors on cars and security mirrors in stores. 15. On the diagram to the right: a) label the normal, incident ray, refracted ray, reflected ray, angle of reflection and angle of refraction incident ray b) Angle of incidence is about 71º Angle of reflection should be 71º (it actually measures about 68º. Sorry, I can t get it to print properly) Angle of refraction is 28º. Ө i normal Ө r reflected ray Remember to measure all angles from the normal!! refracted ray c) does the second medium have a higher or lower refractive Ө R index than the first medium? the second medium must have a higher refractive index because the refracted ray bent toward the normal so the light had to slow down d) how does the speed of the reflected ray compare with the incident ray? the speed of the reflected ray is equal to the speed of the incident ray because the reflected light is travelling in the same medium and it is the medium that determines the speed of light e) how does the speed of the refracted ray compare with the incident ray? the speed of the refracted ray is slower than the speed of the incident ray because the light refracted toward the normal f) What two laws does this diagram portray? the Law of Reflection (the angle of incidence is equal to the angle of reflection when measured from the normal) and the Law of Refraction that states that light will slow down and bend toward the normal when it enters a more optically dense substance 16. Total internal reflection (TIR) takes place when light travels from a substance with a higher refractive index into a substance with a lower refractive index. At the critical angle, the light is refracted back along the surface of the substance. If the incident angle is greater than the critical angle, the light is refracted so much that it is reflected back into the first medium. This is total internal reflection. a) For TIR to occur, the light must move from a substance with a higher refractive index to a substance with a lower refractive index and the angle of incidence must be greater than the critical angle. b) Optical fibres are made of a very fine glass core which is surrounded by a layer of cladding. The cladding (covering) has a lower refractive index than the glass. Light is directed into the optical fibre at an angle larger than the critical angle, so when it hits the edge of the glass, it is totally internally reflected back into the glass fibre. It travels in the glass until it again hits the edge of the glass and is again totally internally reflected back into the glass fibre. The light travels through the glass fibre by bouncing back and forth along the walls until it reaches the end, with very little loss of energy. c) Optical fibres are used to carry information as light for telecommunications (telephone land lines ) and for medical endoscopy- when an optical fibre tube is inserted into a person and light shone along the fibre so a doctor can look inside without doing surgery
17. Calculate the speed of light in corn oil. Show your work. n = c or v = c v n v = 3.0 x 10 8 m/s 1.47 v = 2.04 x 10 8 m/s 18. Light travels from air into plexiglass, hitting the surface at an angle of 36º. What is the angle of refraction? Show a full, organized solution. Substance Refractive Index Air 1.0003 Water (liquid) 1.333 Alcohol 1.361 Corn oil 1.47 Pyrex glass 1.47 Plexiglass 1.49 Crown glass 1.523 Flint glass 1.61 Cubic Zirconium 2.16 Diamond 2.429 Givens: air plexiglass n 1 = 1.0003 n 2 = 1.49 Ө 1 = 36º Ө 2 =? n 1 sine θ 1 = n 2 sine θ 2 (1.0003) (sin 36º) = (1.49) (sin Ө 2 ) (1.0003) (0.588) = (1.49) (sin Ө 2 ) (1.49) (1.49) 0.3946 = sin Ө 2 Ө 2 = 23.24º Therefore, the angle of refraction is 23.24º or 24 º in plexiglass 19. Light travels from alcohol into a cubic zirconium. If the angle of refraction is 27º, what was the angle of incidence? Givens: alcohol cubic zirconium n 1 = 1.361 n 2 = 2.16 Ө 1 =? Ө 2 = 27º n 1 sine θ 1 = n 2 sine θ 2 (1.361) (sin Ө 1 ) = (2.16) (sin 27º) (1.361) (sin Ө 1 ) = (2.16) (0.454 ) (1.361) (1.361) sin Ө 1 = 0.7205 sin Ө 1 = 46.1º Therefore, the angle of incidence is 46.1º or 46º in zirconium
20. Compare near-sightedness and far-sightedness: Medical name for this condition What is wrong in the eye? (2 possibilities) nearsightedness myopia The lens in the eye focuses the image in front of the retina. This can happen because the person s eyeball is too long, or because the lens has too much curvature and converges the light too much. far-sightedness hyperopia The lens in the eye focuses the image behind the retina. This can happen because the person s eyeball is too short, or because the lens does not have enough curvature (is too flat) and does not converge the light enough. What type of lens is used to correct it and why? A diverging lens is used to treat myopia. It spreads out light entering the eye, so that when the eye of the lens causes it to converge, it will focus on the retina. A converging lens is used to treat hyperopia. It converges the light entering the eye just slightly, so that when the eye of the lens converges it again, it will focus on the retina.