Answer to Question #202129 in Optics for xdsss

Question

Total internal reflection in prisms can be used to efficiently bend the light path in optical instruments such as cameras, binoculars, and microscopes.

What is the minimum refractive index of the material the prism is made of in the above diagram? (to 3 s.f)

[Note: the light enters and leaves the prism perpendicular to the faces]

Answer 1

$\sin\frac{\alpha}{2}=\frac{n_1}{n_2}\implies$ $n_2=\frac{n_1}{\sin\frac{\alpha}{2}},$

$n_1=1,~\alpha=110°,$ so

$n_2=1.22.$