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?

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