Question

A thin glass rod is submerged in oil. What is the critical angle for light traveling inside the rod?

Short answer

The critical angle for light traveling inside the rod is${\theta }_c=76.7°$

Step-by-step solution

Total Internal Reflection:

The boundary prevents the ray from refracting. Instead, all of the light reflects back into the prism from the boundary. This is known as total internal reflection, or TIR for short.

Critical Angle:

A critical angle is reached when${\theta }_2=90°$. Because$\sin 90°=1$, Snell’s law$n_1\sin {\theta }_{\mathrm{c}}=n_2\sin 90°$gives the critical angle of incidence as

${\theta }_{\mathrm{c}}={\sin }^{-1}\left(\frac{n_2}{n_1}\right)$

Determine the critical angle for light inside the rod:

Equation that yields the critical angle for light travelling inside the rod is,

${\theta }_c={\sin }^{-1}\left(\frac{n_2}{n_1}\right)$

Substitute the Values:

${\theta }_c={\sin }^{-1}\left(\frac{1.46}{1.50}\right)$

Simplify:

$=76.7°$