Question

7. Sideways Displacement Pro thataray a sheet of plate on the surface of of light incident glass of thickness from the opposite face parallel to its initial direction but displaced ideways, as in Fig. 35-37. Show that, for small angles ofincidence 0, this displacement is given n -1

Answer 1

For small angle, use have n_1 sin theta_1 = n_2 sin theta_2 becomes n_1 theta_1 = n_2 theta_2 for small angles, the displacement of the ray in absence of the glass is X_1 = t theta_1 and for the ray in glass is X_2 = t theta_2 Therefore difference, X = X_1 - X_2 = t (theta_1 - theta_2) = t theta_1 (1- theta_2/theta_1) = t theta_1 (1-n_1/n_2) = > t theta (n-1/n) as n_1 = 1 n_2 = n theta_1 = theta.