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.

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.

Suppose Fig. 32–37 shows a cylindrical rod whose end has a radius of curvature R = 2.0 cm, and the rod is immersed in water with index of refraction of 1.33. The rod has index of refraction 1.49. Find the location and height of the image of an object 2.0 mm high located 23 cm away from the rod.

Two plane mirrors are facing each other 2.2 m apart as in Fig. 32–60. You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of yourself. (a) How far away from you are the first three images of yourself in the mirror in front of you? (b) Are these first three images facing toward you or away from you?

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Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in Fig. E33.1. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?

The indexes of refraction for violet light (λ = 400 nm) and red light (λ= 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 53.5° to the normal. Calculate the angular separation between these two colors of light in the refracted ray.