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Chapter 9: Problem 25

The speed of light in a certain kind of glass is exactly the same as the speed of light in benzene-a liquid. Describe what happens when light passes from benzene into this glass, and vice versa.

Short Answer

Expert verified
Answer: When light passes from benzene to glass and vice versa, there are no changes in its direction and speed due to the equal indices of refraction for both substances. The process of refraction does occur, but the light rays experience no bending while passing through the boundary between benzene and the glass.

Step by step solution

01

Determine the Index of Refraction for Benzene and Glass

To describe what happens when light passes between two different media, we need to know the index of refraction (n) for both benzene and the glass. In this case, the problem states that the speed of light is equal for both benzene and glass. Since the index of refraction (n) is defined as the speed of light in a vacuum (c) divided by the speed of light in a medium (v), and the speeds are equal in benzene and glass, their indices of refraction are also equal.
02

Refraction and Snell's Law

As light travels between two media with different indices of refraction, its direction will change due to a phenomenon called refraction. Snell's law relates the angle of incidence (the angle between the incoming light ray and the normal to the surface) and the angle of refraction (the angle between the refracted light ray and the normal). It is given by: n1 * sin(胃1) = n2 * sin(胃2) where n1 and n2 are the indices of refraction of the first and second media, and 胃1 and 胃2 are the angles of incidence and refraction, respectively.
03

No Change in Direction

Since the indices of refraction are equal for benzene and the glass, Snell's law simplifies to: n * sin(胃1) = n * sin(胃2) So, sin(胃1) = sin(胃2), which means the angle of incidence (胃1) is equal to the angle of refraction (胃2). In other words, there are no changes in the direction of the light as it passes between the benzene and the glass, and vice versa. The light will pass through the boundary without any bending.
04

Speed of Light Remains Constant

As mentioned earlier, the speed of light is the same in both benzene and glass. Therefore, when light passes from benzene to the glass or vice versa, its speed remains constant. There is no change in the speed of light as it travels between the two media.
05

Conclusion

In conclusion, when light passes from benzene to the glass and vice versa, it experiences no change in its direction and speed. The process of refraction does occur, but due to the equal indices of refraction, there will be no bending of the light rays while passing through the boundary between benzene and the glass.

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Most popular questions from this chapter

One sometimes hears the expression, "It was like shooting fish in barrel!" This usually is taken to mean that the task, whatever it was, was easy to complete. But is it really easy to shoot fish in a barrel? Only if you know some optics! Suppose you're in a boat and spy large fish a few meters away. If you want to shoot the fish, how should you aim? Above the image of the fish? Below it? Directly at the image? Explain your choice. (You may assume that the path of the projectile you fire will not be deviated from a straight line upon entering the water, unlike light.

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