Question

n optician directs a ray of light through a transparent medium, toward one surface of an equilateral prism. (The ray travels, and remains in, the plane of the page.) Incident on Surface 1 at an angle θ₁, the ray then encounters Surface 2 from within the prism.

If the angle of incidence at Surface 2 equals θ_c , the critical angle for this prism, what is the original incidence angle, θ₁ (in degrees)? The critical angle in this case is θ_c = 44.0°.

44.0°

44.0°

Answer 1

let n is the refractive index of the medium with which the prism.

n = 1/sin(theta_c)
= 1/sin(44)
= 1.44

Let theta_r is the angle of refraction at first surface

we know, sum the angles in a triangle = 180 degrees

(90 - theta_r) + 60 + (90 - 44) = 180

90 - theta_r + 60 + 90 - 44 = 180

-theta_r + 60 - 44 = 0

theta_r = 60 - 44

= 16 degrees

let theta_i is the angle of incidence at first surface.

use Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

sin(theta_i)/sin(16) = 1.44/1

sin(theta_i) = 1.44*sin(16)

sin(theta_i) = 0.3969

theta_i = sin^-1(0.3969)

= 23.4 degrees <<<<<<<<<---------------------Answer