Question

A glass paperweight with an index of refraction of n = 1.38 sits on a table (in air, n = 1.0) What is the value of the incoming angle θ (not to be confused with the critical angle θc) for which the reflection off of the vertical surface exactly satisfies total internal reflection conditions?

Answer 1

Refer below figure,

Let us first find q₁ , which is critical angle for air-glass interface,

Use equation,

q₁= sin^-1(n_r/n_i)

Here nr= refractive index of refractive medium which is air ,

n_i= refractive index of incident medium which is glass ,

q₁ = sin^-1(1/1.38) = 46.44 deg

Now q2= (90-q₁) = 90-46.44 = 43.56deg is the angle of refraction for top surface of glass for

Use Snell’s law to find q,

Sinq/sinq₂ = n_r/n_i

n_r= refractive index of refractive medium which is glass ,

n_i= refractive index of incident medium which is air ,

q = sin^-1[sin43.56*(1.38/1)] = 72 deg