Porro prism and Refraction of Light

[Nano]

Homework Statement

Ligh is incident normally upon one face of a prism of glass with an index of refraction, n. The light totally reflected as shown in the picture*. What is the minimum value n can have?

*Picture shows a Porro prism (45-45-90 prism)

Homework Equations

n sin(a) = n2 sin (b)
setting b = 90 will solve for the critical angle

The Attempt at a Solution

I guess it has something to do with critical angles. I just don't know how to use the information given. If its incident normally, then does sin(a) = 0? And if the light is not totally internally reflected then, the index of refraction for the prism must be greater than the index of refraction for air (1). so n(prism) > 1.

 

[rl.bhat]

In the porro prism, when the light enters from the smaller side normally, it move without refraction and it incidents on the hypotenuse making an angle of incidence 45 degrees. If this angle happens to the critical angle of the prism glass then the refractive index is given by n = 1/sin(45)