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Chapter 9: Problem 50

The difference in speed between red light and violet light in glass is smaller than the difference in speed between the same two colors in a certain type of plastic. For which material, glass or plastic, would the angular spread of the two colored rays after entering the material obliquely from air be the largest? Why?

Short Answer

Expert verified
Answer: The given type of plastic would produce the largest angular spread between red and violet light after entering obliquely from air.

Step by step solution

01

Understanding the relationship between the speed of light and refractive index

The refractive index (n) of a material is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v): n = c / v. A higher refractive index indicates a slower speed of light in the material, and vice versa.
02

Note the given information about the speed difference of red and violet light in glass and plastic

We are given that the difference in speed between red light and violet light is smaller in glass compared to the difference in the given type of plastic. This means that the difference in refractive index for red and violet light is also smaller in glass than in plastic, as they are inversely proportional.
03

Apply Snell's Law to understand the angular spread of light in different materials

Snell's Law relates the angles of incidence (θ₁) and refraction (θ₂) as well as the refractive indices of two materials: n₁ * sin(θ₁) = n₂ * sin(θ₂). When light enters a material obliquely from air, the difference in refractive index between red and violet light will affect the angle of refraction for each color, resulting in an angular spread between the two colored rays.
04

Determine the material with the largest angular spread

As we established that the difference in refractive index between red and violet light is smaller in glass than in the given type of plastic, the angular spread of the two colored rays after entering the materials obliquely from air will be larger in the plastic. This is because the larger difference in refractive index will result in larger differences in the angles of refraction, as per Snell's Law.
05

Conclusion

The material that would produce the largest angular spread between red and violet light after entering obliquely from air is the given type of plastic. This is due to the larger difference in the refractive index between these two colors of light in the plastic compared to glass, resulting in a larger difference in the angle of refraction and thus a larger angular spread.

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