Question

A thin prism of refracting angle of 2 degrees deviates an incident ray through an angle of 1 degree. Find the value of the refractive index of the material of the prism.

(a) 0.5
(b) 1.5
(c) 2.5
(d) 3.5

Answer 1

The refractive index of the material of the prism can be found using the formula n = sin((A + D)/2) / sin(A/2), where A is the refracting angle and D is the angle by which the incident ray deviates.

By substituting the given values, we find that the refractive index is approximately 1.186.

Step-by-step explanation:

To find the refractive index of the material of the prism, we can use the formula:

Refractive index (n) = sin((A + D)/2) / sin(A/2)

Where A is the refracting angle (2 degrees) and D is the angle by which the incident ray deviates (1 degree).

Substituting the values, we get:

Refractive index (n) = sin((2 + 1)/2) / sin(2/2)

Refractive index (n) = sin(1.5) / sin(1)

Using a calculator, we can find that sin(1.5) ≈ 0.997 and sin(1) ≈ 0.841.

Therefore, the refractive index (n) ≈ 0.997 / 0.841 ≈ 1.186.

Since none of the given options are close to 1.186, we cannot determine the exact value.