A ray of light is incident on the left vertical face of a glass cube of refractive index $μ_2$, as shown in figure. The plane of incident is the plane of the page, and the cube is surrounded by liquid $(μ_1)$. What is the largest angle of incidence $θ_1$ for which total internal reflection occurs at the top surface?

$\sin θ_1=\sqrt{(\frac{μ_2}{μ_1})^2-1}$

Consider A Point

Applying Snell’s law,

$μ_1\sin θ_1 = μ_2\sin θ_2$ …(1)

But $θ_2 = 90° – θ_c$

$∴ \cos θ_2 = \sin θ_c = \frac{μ_1}{μ_2}$   …(2)

Elimination of $θ_2$ between (1) and (2), we get

$∴\sin θ_1=\sqrt{(\frac{μ_2}{μ_1})^2-1}$