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PHYS 202 DRILL HOMEWORK PROBLEMS
PART 3
D3-1. Red light with a free-space wavelength of 650 nm and blue light with a frequency of 7.32x1014 Hz are
traveling in air. Find the frequency of the red light and the wavelength of the blue light. Which has the
longer wavelength? Which has the higher frequency?
[4.62x1014 Hz, 410 nm;
red has longer wavelength, blue has higher frequency]
D3-2. A beam of light is traveling in glass with an index of 1.5. The wavelength of the light in the glass is 400
nm. Find the frequency of the light, the speed of the light in the glass, and its free-space wavelength.
[5x1014 Hz, 2x108 m/s, 600 nm]
D3-3. A beam of light is traveling in air and enters a piece of glass with an index of 1.6 at an angle of incidence
of 20. The wavelength of the light in air is 520 nm. Find the angle that the transmitted light beam makes
with the surface normal as well as the wavelength and frequency of the light inside the glass.
[12.3, 325 nm, 5.77x1014 Hz]
D3-4. Light in air hits a piece of glass with an angle of incidence of 30. Find the angle of reflection of the
reflected light and the angle of refraction for the transmitted light if the index of the glass is 1.57.
[30, 18.6]
D3-5. Light is traveling in a piece of glass and hits the top of it with an angle of incidence of 22. Some of the
light refracts into the air with an angle of refraction of 38. Find the refractive index of the glass.
[1.643]
D3-6. When light traveling in air enters water, does the light bend towards the surface normal or away from it?
What about light traveling in glass with an index of 1.6 that enters water?
[towards normal; away from normal]
D3-7. A block of glass has an index of 1.47. Find the critical angle at the glass-air interface. For total internal
reflection to occur, does the light have to be in the air and hit the glass or be in the glass and hit the air?
Does the angle of incidence have to be smaller or larger than the critical angle?
[42.9, in glass and hit air, larger]
D3-8. Light from an underwater lamp hits the water-air interface at an angle of incidence of 52. Will any of
the light be transmitted into the air? Assume a refractive index of 1.33 for the water.
[no, TIR occurs]
D3-9. You look into a pond and see a fish almost directly below you that looks like it is about 30 cm beneath
the surface. About how deep is the actual fish?
[40 cm]
D3-10. Two lenses are made out of glass with an index of refraction of 1.52. Both lenses have front surfaces
with a radius of curvature of +60 mm. The radius of curvature of the back surface of lens A is –30 mm.
That of lens B is +30 mm. Find the focal lengths of the two lenses when they are used in air.
[Lens A +38.5 mm, Lens B –115 mm]
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D3-11. A lens with an index of 1.65 has a focal length of +5 cm in air. One side of the lens is flat. What is the
size of the radius of curvature of the other side of the lens? Is the lens thinner or thicker in the middle?
[3.25 cm, thicker in the middle]
D3-12. An object is placed 50 cm from a converging lens with a focal length of 10 cm. Find how far the image
is formed from the lens and the lateral magnification. Is this lens acting as a camera, projector, or
magnifying glass? Is the image on the same side of the lens as the object or the opposite side?
[12.5 cm, -0.25x, camera, opposite]
D3-13. An object is placed 15 cm from a converging lens with a focal length of 10 cm. Find how far the image
is formed from the lens and the lateral magnification. Is this lens acting as a camera, projector, or
magnifying glass? Is the image on the same side of the lens as the object or the opposite side?
[30 cm, -2x, projector, opposite]
D3-14. An object is placed 8 cm from a converging lens with a focal length of 10 cm. Find how far the image is
formed from the lens and the lateral magnification. Is this lens acting as a camera, projector, or
magnifying glass? Is the image on the same side of the lens as the object or the opposite side?
[40 cm, +5, magnifying glass, same]
D3-15. The lens in the previous problem is acting as a magnifying glass. Find the angular magnification of the
lens. What is the best angular magnification that one could get from this lens? How far from the lens
should the object be placed to achieve this magnification?
[3.125x, 3.5x, 7.14 cm]
D3-16. An object is placed 15 cm from a diverging lens with a focal length of -10 cm. Find how far the image is
formed from the lens and the lateral magnification. Is the image on the same side of the lens as the object
or the opposite side?
[6 cm, +0.4x, same]
D3-17. A person’s eye is hyperopic and has a near point of 75 cm. Does this eye need a positive or negative
lens to correct its vision? Find the focal length and lens power in diopters for the corrective lens.
[positive, 37.5 cm, +2.67 diopters]
D3-18. A person’s eye is myopic and has a far point of 125 cm. Does this eye need a positive or negative lens to
correct its vision? Find the focal length and lens power in diopters for the corrective lens.
[negative, -125 cm, -0.8 diopters]
D3-19. Light with a wavelength of 600 nm is sent through two vertical slits separated by 0.5 mm. The
interference pattern is observed on a screen 3 meters away from the slits. Find the separation of the centers
of the bright fringes. Find the separation of the centers of the dark fringes.
[both are separated by 3.6 mm]
D3-20. Monochromatic light is sent through a pair of slits separated by 1 mm and the resulting interference
pattern is viewed on a screen 5 meters away. The spacing between the centers of the bright fringes is 2.3
mm. Find the wavelength of the light. What color is the light?
[460 nm, blue]
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D3-21. White light is sent through a grating with a grating constant of 800 lines/mm. What is the distance
between two consecutive lines? At what angle is light with a wavelength of 500 nm sent in the first-order
diffraction?
[1250 nm, 23.6]
D3-22. The lines on a transmission grating are separated by 1000 nm. Find the first-order diffraction angles of
light with the following wavelengths: 400 nm, 500 nm, and 600 nm. Does blue light have a smaller or
larger first-order diffraction angle that red light?
[23.6, 30.0, 36.9, smaller]
D3-23. Part of a soap bubble appears green (~550 nm) when viewed in reflected light. About how thin is the
soap film in this part of the bubble? Assume that the film is as thin as it can be to reflect the green light.
[103.4 nm]
D3-24. A 105 nm coating with an index of 1.38 is put onto a glass lens with an index of 1.65. What visible
wavelength will be strongly transmitted through the lens because of this coating?
[580 nm]
D3-25. A lens with a focal length of 10 cm has a diameter of 2.5 cm. Find its diffraction-limited resolution
angle at a wavelength of 580 nm. Express the angle in radians and arc seconds. Would using red light or
blue light improve its resolution capability?
[2.8x10-5 = 5.8”, blue]
D3-26. An object is placed 3 meters from the lens in the previous problem and an image is formed. Find the
minimum separation distances of two resolvable points on the object and on the image.
[84 m on object, 3 m on image]
D3-27. The pupil of your eye is opened to a diameter of 3 mm. What is the approximate diffraction-limited
resolution angle of your eye? Use a free-space wavelength of 580 nm and a refractive index of 1.33 for the
aqueous and vitreous humor of the eyeball. Can this eye resolve two points that are 1 mm apart on an
object that is 10 meters away?
[1.77x10-4 rad; no, dmin = 1.77 mm]
D3-28. Light is linearly polarized with its electric field axis in a direction of 30. It is sent through a dichroic
polarizer whose polarization axis can be sent to any angle. Rank the following settings from the one that
will pass the most to the one that will pass the least light: 0, 30, 45, 120.
[30, 45, 0, 120]
D3-29. What angle should there be between the polarization axes of two polarizers if you want 40% of the light
intensity through the first polarizer to pass through the second polarizer?
[50.8]
D3-30. Unpolarized light is traveling in air. It reflects off a piece of glass at an incident angle of 59 and is
completely linearly polarized. What must be the refractive index of the glass?
[1.66]
D3-31. Unpolarized light traveling in air reflects off of the surface of a pond. The pond water has an index of
1.33. Which angle of incidence will have more of the reflected light linearly polarized: 30, 50, or 70?
[50 since it is closest to 53]