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Chapter 9: Problem 51

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: Plastic

Step by step solution

01

Understand Snell's Law

Snell's law relates the angles of incidence (θ₁) and refraction (θ₂) to their refractive indices (n₁ and n₂, respectively), as: n₁ * sin(θ₁) = n₂ * sin(θ₂)
02

Compare Refractive Indices Based on Given Information

We are given that the difference in speed between red light and violet light in glass is smaller than that in plastic. Since the refractive index is inversely proportional to the speed of light in a material, a smaller difference in speed implies that the difference in refractive indices between red and violet light would also be smaller for glass than for plastic.
03

Apply Snell's Law to Evaluate Angular Spread

For both glass and plastic, as the light enters the materials obliquely from air (n₁ = 1), we can use Snell's law to compare the angular spread between red and violet light. For each material: 1 * sin(θ₁) = n₂(red) * sin(θ₂_red) 1 * sin(θ₁) = n₂(violet) * sin(θ₂_violet) As the difference in refractive indices between red and violet light is larger for plastic than glass, the difference between the angles of refraction, θ₂_red and θ₂_violet, would be larger for plastic.
04

Conclusion

Based on the analysis above, the angular spread of the two colored rays (red and violet light) after entering the material obliquely from air would be the largest for the plastic. This is because the difference in refractive indices between red and violet light is larger for plastic than for glass, leading to a larger difference between their angles of refraction.

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