Chapter 23, Problem 14Q

To determine

(a) To determine:

The material which has the largest index of refraction, if a ray of light is refracted through three different materials

Answer to Problem 14Q

Solution:

When a light ray bends towards normal after refraction, then it has moved from a lower refractive index medium to a higher refractive index medium. When light ray bends away from the normal after refraction, it has moved from a higher refractive index medium to a lower refractive index medium.

The largest refractive indices of materials 1, 2, 3 are in the order of material 2 > material 1 > material 3

Explanation of Solution

Given:

A ray of light is refracted through three different materials

Formula used:

The Snell’s law describes that, when the light passes from one transparent medium into another with a different index of refraction, it bents and is given by

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

Where,

${\theta }_1\text{ and }{\theta }_2$ the angle of incidence and the angle of refraction;

$n_1\text{ and }{n}_2$ are the respective indices of refraction in the materials.

Calculation:

Snell’s law shows that if $n_2>n_1$ then ${\theta }_2<{\theta }_1$.

Thus, if light enters a medium where n is greater (and its speed is less), the ray is bent towards the normal. And if $n_2<n_1$ then ${\theta }_1<{\theta }_2$, so the ray bends away from the normal.

The light bent towards the normal in the material 2 with respect to 1 and it bent away from the normal with respect to 2.

Analyzing the given specimen, the light bent towards the normal is greater in material 2 than material 1. And, in the material 3, the light bents away from the normal. Hence, material 3 has the least refractive index and material 2 has the largest index than the material 2. Hence, the materials are listed in the order of the largest refractive indices as material 2 > material 1 > material 3.

To determine

(b) To determine:

The material which has the smallest index of refraction if a ray of light is refracted through three different materials

Answer to Problem 14Q

Solution:

The materials are listed in the order of the smallest refractive indices as material 3 < material 1 < material 2

Explanation of Solution

A ray of light is refracted through three different materials.

When a light ray bends towards normal after refraction, then it has moved from a lower refractive index medium to a higher refractive index medium. When light ray bends away from the normal after refraction, it has moved from a higher refractive index medium to a lower refractive index medium.

Analyzing the given specimen, the light bent towards the normal is greater in material 2 than material 1. And, in the material 3, the light bents away from the normal. Hence, material 3 has the least refractive index and material 2 has the largest index than the material 2. Hence, the materials are listed in the order of the smallest refractive indices as material 3 < material 1 < material 2