33. Geometric Optics

A light beam travels at 1.94 × 10⁸ m/s in quartz. The wavelength of the light in quartz is 355 nm. If this same light travels through air, what is its wavelength there?

A horizontal meter stick is centered at the bottom of a 3.0-m-deep, 3.0-m-wide pool of water. Suppose you place your eye just above the edge of the pool and look along the direction of the meter stick. What angle do you observe between the two ends of the meter stick if the pool is (a) empty and (b) completely filled with water?

A beam of light is emitted 7.7 cm beneath the surface of a liquid and strikes the surface 7.2 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid?

(I) The speed of light in ice is 2.29 x 10⁸ m/s. What is the index of refraction of ice?

A flashlight beam strikes the surface of a pane of glass (n = 1.56) at a 69° angle to the normal. What is the angle of refraction?

A longitudinal earthquake wave strikes a boundary between two types of rock at a 41° angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus (Section 15–2)is the same for both types of rock, determine the angle of refraction.

The label on a laser says it produces light of wavelength 670 nm. The laser beam passes through a block of plastic for which n = 1.57. What is the wavelength of the light inside the plastic?

An astronaut is exploring an unknown planet when she accidentally drops an oxygen canister into a 1.50-m-deep pool filled with an unknown liquid. Although she dropped the canister 21 cm from the edge, it appears to be 31 cm away when she peers in from the edge. What is the liquid's index of refraction? Assume that the planet's atmosphere is similar to earth's.

When light passes through a prism, the angle that the refracted ray makes relative to the incident ray is called the deviation angle δ, Fig. 32–64. Show that this angle is a minimum when the ray passes through the prism symmetrically, perpendicular to the bisector of the apex angle Φ, and show that the minimum deviation angle, δ_m, is related to the prism’s index of refraction n by

$n=\frac{\sin \frac{1}{2}(\varphi +{\delta }_m)}{\sin \varphi /2}.$

[Hint: For θ in radians, $\left(d/d\theta \right)\left({\sin }^{-1}\theta \right)=1/\sqrt{1-{\theta }^2}$.]

(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 41.3° angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2° from the normal, what is the refractive index of the unknown liquid?

A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of I) of scattered light in the middle of the red part of the spectrum.