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Chapter 5: Q18E (page 1105)

A beam of light is traveling inside a solid glass cube that has index of refraction 1.62. It strikes the surface of the cube from the inside. (a) If the cube is in air, at what minimum angle with the normal inside the glass will this light not enter the air at this surface? (b) What would be the minimum angle in part (a) if the cube were immersed in water?

Short Answer

Expert verified
  1. The minimum angle with the normal side when the cube is in the air38.118掳
  2. The minimum angle when the cube is immersed in water55.37掳

Step by step solution

01

Snell’s law

Snell's law determines the degree of refraction as well as the relationship between the angle of incidence, angle of refraction, and refractive indices of two media.

Here;

Critical Angle-Beyond which light rays traveling through a thicker media to the surface of a less dense medium is no longer refracted but completely reflected

Total Internal Reflection-When the angle of incidence surpasses the critical angle, a light ray reaches an interface with a less dense material and is completely reflected.

02

Minimum angle with the normal side when cube in air

Applying Snell鈥檚 law;

Hence, the minimum angle with the normal side when the cube is in the air38.118掳

03

Minimum angle when cube immersed in water

Applying Snell鈥檚 law;

Hence, the minimum angle when the cube is immersed in water55.37掳

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Most popular questions from this chapter

On December 26, 2004, a violent earthquake of magnitude 9.1 occurred off the coast of Sumatra. This quake triggered a huge tsunami (similar to a tidal wave) that killed more than 150,000 people. Scientists observing the wave on the open ocean measured the time between crests to be 1.0 h and the speed of the wave to be 800 km>h. Computer models of the evolution of this enormous wave showed that it bent around the continents and spread to all the oceans of the earth. When the wave reached the gaps between continents, it diffracted between them as through a slit.

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(b) The distance between the southern tip of Africa and northern Antarctica is about 4500 km, while the distance between the southern end of Australia and Antarctica is about 3700 km. As an approximation, we can model this wave鈥檚 behavior by using Fraunhofer diffraction. Find the smallest angle away from the central maximum for which the waves would cancel after going through each of these continental gaps.

A beam of light goes from one material into another. On physical grounds, explain why the wavelength changes but the frequency and period do not.

Interference can occur in thin films. Why is it important that the films be thin? Why don鈥檛 you get these effects with a relatively thick film? Where should you put the dividing line between 鈥渢hin鈥� and 鈥渢hick鈥�? Explain your reasoning.

Figure 31.12 (Section 31.2) shows a loudspeaker system. Low-frequency sounds are produced by the woofer, which is a speaker with a large diameter; the tweeter, a speaker with a smaller diameter, produces high-frequency sounds. Use diffraction ideas to explain why the tweeter is more effective for distributing high-frequency sounds uniformly over a room than is the woofer.

Huygens鈥檚 principle also applies to sound waves. During the day, the temperature of the atmosphere decreases with increasing altitude above the ground. But at night, when the ground cools, there is a layer of air just above the surface in which the temperature increaseswith altitude. Use this to explain why sound waves from distant sources can be heard more clearly at night than in the daytime. (Hint:The speed of sound increases with increasing temperature. Use the ideas displayed in Fig. 33.36 for light.)
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