33. Geometric Optics

A light ray strikes a horizontal surface at a 60° angle. The reflected ray then strikes a wall 2.5m above the reflective surface. How far is the wall from the point where the incident light ray strikes the surface?

At what angle ϕ should the laser beam in FIGURE EX34.6 be aimed at the mirrored ceiling in order to hit the midpoint of the far wall?

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

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?

Two polarizers are oriented at 44.0° to one another. Light polarized at a 22.0° angle to each polarizer passes through both. What is the transmitted intensity (%)?

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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What is the distance, d, between the incoming and outgoing rays?

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.

A 75 kW radio transmitter emits 550 kHz radio waves uniformly in all directions. At what rate do photons strike a 1.5-m-tall, 3.0-mm-diameter antenna that is 15 km away?

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

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.

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?

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

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.

(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.