Homework #6 Physics 112-4 Fall 2011 p1
Homework #6: optics
Chapter 30: Reflection and Refraction
Page #541:
#2: Why does a spoon appear bent when it’s in a glass of water?
#3: Why do a diamond and an identically shaped piece of glass sparkle differently?
#7: Why can’t you walk to the end of the rainbow?
#11: Through what angle should you rotate a mirror so that a reflected ray rotates through 30°?
#16: Information on a compact disk is stored in “pits” whose depth is essentially one-fourth the
wavelength of the laser light used to “read” the information. The wavelength is 780nm in air, but
the wavelength on the pit depth is based is measured in the n=1.55 plastic that makes up most of
the disk. Find the pit depth.
#22: Find the critical angle for total internal reflection in (a) ice (n=1.309), (b) polystyrene
(n=1.49), and (c) rutile, also known as titanium oxide, (n=2.62), when the surrounding medium is
air.
##26: Blue and red laser beams strike an air-glass interface with incidence angle 50°. If the glass
has refractive indices of 1.680 for blue light and 1.621 for red light, what will be the angle
between the two beams in the glass?
Page #542:
#29: The refractive index of the human cornea is 1.40. If 550mm light strikes a cornea at
incidence angle 25°, find (a) the angle of refraction and (b) the wavelength in the cornea.
Page #543:
#60: You’re an automotive engineer charged with evaluating safety glass, which is made by
bonding a layer of flexible plastic between two layers of glass, thus eliminating dangerous glass
fragments during accidents. A new product uses glass with refractive index n=1.55 and plastic
with n=1.48. You’re asked to determine whether total internal reflection at the glass-plastic
interface could cause problems with visibility. What do you conclude and why?
Chapter 31: Images and Optical Instruments
Page #561:
#1: How can you see a virtual image when it’s not “really there”?
#5: What is the meaning of negative object distance? Negative focal length?
##12: Does a fish in a spherical bowl appear larger or smaller than it actually is?
##17: A shoe store uses small floor-level mirrors to let customers view prospective purchases. At
what angle should such a mirror be inclined so that a person standing 50cm from the mirror with
eyes 140cm off the floor can see her feet?
Homework #6 Physics 112-4 Fall 2011 p2
#27: A magnifying glass enlarges print by 50% when it is 90cm from a page. What’s the focal
length?
#35: You’re an optometrist helping a nearsighted patient who claims he can’t see clearly beyond
80cm. Prescribe a lens that will put the images of a distant object at 80cm, giving you patient
clear vision at all distances beyond the normal near point.
Page #562:
#66: You are taking a photography class, working with a camera whose zoon lens covers the
focal-length range 38-110mm. Your instructor asks you to compare the sizes of the images of a
distant object when photographed at the two zoom extremes. Your answer?
#71: You stand with your nose 6.0cm from the surface of a reflecting ball, and your nose’s image
appear three-quarters full size. What is the ball’s diameter?
Page #563:
#75: Show that identical objects placed equal distances on either side of the focal point of a
concave mirror or converging lens produce images of equal size. Are the images of the same
type?
Chapter 32: Interference and Diffraction
Page #581:
#1: A prism bends blue light more than red. Is the same true of a diffraction grating?
#5: You can hear around corners, but you can’t see around corners. Why?
#14: The 546nm green line of gaseous mercury falls on a double-slit apparatus. If the fifth dark
fringe is at 0.113° from the centerline, what’s the slit separation?
#21: Find the minimum thickness of a soap film (n=1.333) in which 550nm light will undergo
constructive interference.
#32: What is the longest wavelength of light that you could use to resolve a structure with angular
diameter 0.44mrad, using a microscope with aperture 1.2mm in diameter?
Page #582:
#61: While driving at night, your eyes’ irises dilate to 3.1mm diameter. If your vision were
diffraction limited, what would be the greatest distance at which you could see as distinct the two
headlights of an oncoming car 1.5m apart. Take λ=550nm.