Question

Light of frequency 6.0 x 10¹⁴ hertz strikes a glass/air boundary at an angle of incidence θ₁.  The ray is partially reflected and partially refracted at the boundary, as shown. The index of refraction of this glass is 1.6 for light of this frequency.

a. Determine the value of θ₃ if θ₁ = 30°.

b.  Determine the value of θ₂ if θ₁ = 30°.

c. Determine the speed of this light in the glass.

d. Determine the wavelength of this light in the glass.

e. What is the largest value of θ₁ that will result in a refracted ray?

Answer 1

(a) Law of reflection, angle of incidence = angle of reflection. θ₃ = 30°

(b) n_i sin θ_i = n_r sin θ_r, … (1.6) sin 30 = 1 sin θ₂ … θ₂ = 53.1°

(c) n = c /v (1.6) = 3x10⁸ / v   v = 1.875x10⁸ m/s

(d) First c = f_air λ_air n₁ λ₁ = n₂ λ₂ … n_air λ_air = n_glass λ_glass … n_air (c/f_air) = n_g λ_g … λ_g = 3.125 x 10^–7 m

(e) Determine critical angle, glass to air.  n_i sin θ_c = n_r sin 90 (1.6) sin θ_c = (1) θ_c = 38.68°

Any angle larger than 38.68° will cause total reflection.