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Chapter 5: Q51P (page 1214)

A thin slit illuminated by light of frequency f produces its first dark band at ±38.2° in air. When the entire apparatus (slit, screen, and space in between) is immersed in an unknown transparent liquid, the slit’s first dark bands occur instead at ±21.6°. Find the refractive index of the liquid.

Short Answer

Expert verified

The refractive index is 1.68

Step by step solution

01

Refractive index

If i is the angle of incidence of a ray in a vacuum (the angle between the incoming ray and the perpendicular to the surface of a medium, called the normal), and r is the angle of refraction (the angle between the ray in the medium and the normal), the refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction;

02

Refractive index of the liquid

Using

Combining it with

In the case of air and m=1;

In the case of liquid;

So, the refractive index is;

Hence, the refractive index is 1.68

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Most popular questions from this chapter

Huygens’s 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.)

A spherical mirror is cut in half horizontally. Will an image be formed by the bottom half of the mirror? If so, where will the image be formed?

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