Question #43200

A monochromatic light beam is incident at an angle $i = 60^\circ$ on a semiconductor slab of thickness $t = 9\sqrt{3} \text{ mm}$. At an initial temperature $T_0 = 300 \text{ K}$, the refractive index of the slab is $n_0 = \sqrt{3}$ and its optical band gap is $E_{g0} = 1.5 \text{ eV}$. The refractive index $n$ and the band gap $E_g$ of the material are related by Moss's rule: $n^4 E_g = \text{constant}$. In the given temperature range, the band gap decreases linearly with temperature as $E_g(T) = E_{g0} - \beta (T - T_0)$, where $\beta = 2 \times 10^{-4} \text{ eV/K}$. If the temperature of the slab is increased to $T = 350 \text{ K}$, what is the approximate change in the lateral shift of the transmitted beam? (Assume the thermal expansion of the slab is negligible).