33. Geometric Optics

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to (a) 1/3, (b) 1/10?

At what angle above the horizon is the Sun when light reflecting off a smooth lake is polarized most strongly?

What is Brewster’s angle for an air-glass (n = 1.56) surface? Specify two answers.

What would Brewster’s angle be for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface.

Suppose you are 96 cm from a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 4.5 mm?

As early morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f-number from f/5.6 to f/16. By what factor had the sunlight intensity increased during that time?

"(II) Two plane mirrors meet at a 135° angle, Fig. 32–47. If light rays strike one mirror at 32° as shown, at what angle θ do they leave the second mirror?

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A person whose eyes are 1.64 m above the floor stands 2.60 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor, Fig. 32–48. What is the horizontal distance x, from the base of the wall supporting the mirror to the nearest point on the floor that can be seen reflected in the mirror?

(II) The critical angle for total internal reflection at a boundary between two materials is 48°. What is Brewster’s angle at this boundary? Give two answers, one for each material.

Suppose that you want to take a photograph of yourself as you look at your image in a mirror 2.4 m away. For what distance should the camera lens be focused?

Show that if two plane mirrors meet at an angle Φ, a single ray reflected successively from both mirrors is deflected through an angle of 2Φ independent of the incident angle. Assume Φ < 90° and that only two reflections, one from each mirror, take place.

What percent of visible light is reflected from plain glass? Assume your answer refers to transmission through each surface, front and back. How does the presence of multiple lenses in a good camera degrade the image? What is suggested in Section 34–5 to reduce this reflection? Explain in words, and sketch how this solution works. For a 6-element glass lens in air, about how much improvement does this solution provide?

You hold a small flat mirror 0.50 m in front of you and can see your reflection twice in that mirror because there is a full-length mirror 1.0 m behind you (Fig. 32–71). Determine the distance of each image from you.

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(II) A ray of light, after entering a light fiber, reflects at an angle of 14.5° with the long axis of the fiber, as in Fig. 32–57. Calculate the distance along the axis of the fiber that the light ray travels between successive reflections off the sides of the fiber. Assume that the fiber has an index of refraction of 1.55 and is 1.60 x 10^-4 m in diameter.

X-rays of wavelength 0.10 nm fall on a microcrystalline powder sample. The sample is located 15 cm from a photographic sensor. The crystal structure of the sample has an atomic spacing of 0.22 nm. Calculate the radii of the diffraction rings corresponding to first- and second-order scattering. Note in Fig. 35–28 that the X-ray beam is deflected through an angle 2Φ.