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Chapter 9: Problem 23

Describe how the path of a ray is deviated as it passes (at an angle) from one medium into a second medium in which the speed of light is lower. Contrast this with the case when the speed of light in the second medium is higher.

Short Answer

Expert verified
Answer: When the speed of light is lower in the second medium, the path bends toward the normal (imaginary line perpendicular to the boundary) as the angle of refraction is less than the angle of incidence. When the speed of light is higher in the second medium, the path bends away from the normal as the angle of refraction is greater than the angle of incidence.

Step by step solution

01

Understanding Refraction and Snell's Law

Refraction is the bending of a light ray as it passes from one medium to another at an angle. This change in direction is due to the variation in the speed of light in different media. Snell's Law relates the angle of incidence (θ₁) with the angle of refraction (θ₂) and the refractive indices of the two media (n₁ and n₂). Mathematically, it is expressed as: n₁ * sin(θ₁) = n₂ * sin(θ₂)
02

Case 1 - Speed of Light is Lower in the Second Medium

When the speed of light is lower in the second medium, the refractive index of the second medium (n₂) is higher than the refractive index of the first medium (n₁). Using Snell's Law, since n₁ * sin(θ₁) = n₂ * sin(θ₂), it means that sin(θ₂) will be less than sin(θ₁), indicating that θ₂ < θ₁. The angle of refraction (θ₂) will be less than the angle of incidence (θ₁). The path of the light ray will bend toward the normal, which is the imaginary line perpendicular to the boundary between the two media.
03

Case 2 - Speed of Light is Higher in the Second Medium

When the speed of light is higher in the second medium, the refractive index of the second medium (n₂) is lower than the refractive index of the first medium (n₁). Using Snell's Law, since n₁ * sin(θ₁) = n₂ * sin(θ₂), it means that sin(θ₂) will be greater than sin(θ₁), indicating that θ₂ > θ₁. The angle of refraction (θ₂) will be greater than the angle of incidence (θ₁). The path of the light ray will bend away from the normal, which is the imaginary line perpendicular to the boundary between the two media.

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