Question

A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0°. It is observed that the reflected and refracted beams form an angle of 90.0°. What is the index of refraction of this material?

Answer 1

Answer:

the index of refraction for the transparent material is 1.48

Explanation:

let n1 = 1.0 be the refractive index of air and n2 be the refractive index of the trasnparent material.

then:

Snell's Law state that:

n1×sin(∅1) = n2×sin(∅2)

where ∅1 = 56.0° is the angle of incidence and  ∅2 = 90 - 56.0 = 34° be the angle refraction.

n1×sin(∅1) = n2×sin(∅2)

          n2 = n1×sin(∅1)/sin(∅2)

               =  (1.0)×sin(56.0°)/sin(34.0°)

               =  1.48

Therefore, the index of refraction for the transparent material is 1.48