Question #43136

An isosceles glass prism has an apex angle $A = 60^\circ$ (the angle between its two equal sides) at an initial temperature $T_0$. The base of the prism has a linear thermal expansion coefficient $\alpha_1 = 8\sqrt{3} \times 10^{-6} \text{ K}^{-1}$, while its two equal sides have a linear thermal expansion coefficient $\alpha_2 = 3\sqrt{3} \times 10^{-6} \text{ K}^{-1}$. At $T_0$, the refractive index of the glass is $n = \sqrt{3}$ and its thermo-optic coefficient is $\frac{dn}{dT} = -3 \times 10^{-5} \text{ K}^{-1}$. The prism has a mass $m = 100 \text{ g}$ and a specific heat capacity $c = 400 \text{ J kg}^{-1} \text{K}^{-1}$. A laser beam of power $P = 20 \text{ W}$ is completely absorbed by the prism for a duration $\Delta t = 100 \text{ s}$. Assuming no heat is lost to the surroundings and the temperature of the prism remains uniform, what is the magnitude of the change in the angle of minimum deviation, $|\Delta \delta_m|$?