Is There an Error in the Angle Calculation for the Emergent Ray from a Prism?

[jemerlia]

Homework Statement

A ray of monochromatic yellow light is incident in air on an
equilateral triangular glass prism. This ray is in the same plane as
the equilateral triangular cross section of the prism; the angle
between the ray and the prism face is 60°, and the refractive index
of the glass is 1.54 for this light.

Find the angle the emergent ray makes with the prism face at
which it emerges. Illustrate your answer with a diagram.

The given answer is 60 degrees. The problem appears straightforward but it appears impossible to get the required result with the given data. Please check my solution and comment...

Homework Equations

Snells law: n1*sin theta1 = n2 sin theta 2

The Attempt at a Solution

For angle of refraction of the incident light - from air into the prism:

sin r = sin 30/1.54, r = 18.94 degrees

The angle of incidence upon striking the internal glass surface = 60-18.94

Therefore the angle of refraction - from glass back into the air:

= asin(1.54 * sin(60-18.94))

The difficulty is that the inner sin function gives a value > 1

Have I done something wrong?

 

[rl.bhat]

60-18.94 = 41.06 is greater then the critical angle. Now draw the ray diagram and find the angle of incidence of the total internal reflected ray on the prism face.

 

[jemerlia]

Quite so... many thanks for your help!