•1 In Fig. 35-31, a light wave alongray r, reflects once from a mirror anda light wave along ray r, reflects twicefrom that same mirror and once froma tiny mirror at distance L from thebigger mirror. (Neglect the slight tilt Figure 35-31 Problems 1 and 2.of the rays.) The waves have wave-length 620 nm and are initially in phase. (a) What is the smallest valueof L that puts the final light waves exactly out of phase? (b) With thetiny mirror initially at that value of L, how far must it be moved awayfrom the bigger mirror to again put the final waves out of phase?

(a) Ray 1 travels a distance 2L whereas ray 2 travels a distance 4L. Thus, the path difference…

Answered: •1 In Fig. 35-31, a light wave along…

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter35: The Nature Of Light And The Principles Of Ray Optics

Section: Chapter Questions

Problem 35.81CP

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While using a Michelson interferometer (shown in Fig. 37.13), you see a dark circle at the center of the interference pattern, (i) As you gradually move the light source toward the central mirror M0, through a distance /2, what do you see? (a) There is no change in the pattern, (b) The dark circle changes into a bright circle. (c) The dark circle changes into a bright circle and then back into a dark circle. (d) The dark circle changes into a bright circle, then into a dark circle, and then into a bright circle. (ii) As you gradually move the moving mirror toward the central mirror M0, through a distance /2, what tit) you see? Choose from the same possibilities.
Show that if you have three polarizing filters, with the second at an angle of 45° to the first and the third at an angle of 90.0° to the first, the intensity of light passed by the first will be reduced to 25.0% of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)
Prove that, if I is the intensity of light transmitted by two polarizing filters with axes at an angle and I is the intensity when the axes are at an angle 90.0, then I+I=I0, the original intensity. (Hint: Use the trigonometric identities cos(90.0)=sin and cos2+sin2=1 .)
If b is Brewster's angle for light reflected from the top of an interface between two substances, and b is Brewster's angle for light reflected from below, prove that b+b=90.0.
Prove that if I is the intensity of light transmitted by two polarizing filters with axes at an angle and I’ is the intensity when the axes are at an angle 90.0, then I+I=I0, the original intensity. (Hint: Use the trigonometric identities cos 90.0=sinand cos2sin2=1 .)
Can a sound wave in air be polarized? Explain.
A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of refraction of 1.40.
A 65-fringe shift results in a Michelson interferometer when a 42.0-µm film made of an unknown material is placed in one arm. The light source has wavelength 632.9 nm. Identify the material using the indices of refraction found in Table 1.1.
Two polarizing sheets P1 and P2 are placed together with their transmission axes oriented at an angle to each other. What is when only 25% of the maximum transmitted light intensity passes through them?
Check Your Understanding Although m, the number of fringes observed, is an integer, which is often regarded as having zero uncertainty, in practical terms, it is all too easy to lose track when counting fringes. In Example 3.6, if you estimate that you might have missed as many as five fringes when you reported m=122 fringes, (a) is the value for the index of refraction worked out in Example 3.6 too large or too small? (b) By how much?
You are told not to shoot until you see the whites of their eyes. If the eyes are separated by 6.5 cm and the diameter of your pupil is 5.0 mm, at what distance can you resolve the two eyes using light of wavelength 555 nm?
Many cells are transparent anti colorless. Structures of great interest in biology and medicine can be practically invisible to ordinary microscopy. To indicate the size and shape of cell structures, an interference micro-scope reveals a difference in index of refraction as a shift in interference fringes. The idea is exemplified in the following problem. An air wedge is formed between two glass plates in contact along one edge and slightly separated at the opposite edge as in Figure P37.37. When the plates are illuminated with monochromatic light from above, the reflected light has 85 dark fringes. Calculate the number of dark fringes that appear if water (n = 1.33) replaces the air between the plates.

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