A glass rod of rectangular cross-section is bent into the shape shown in the figure below. A parallel beam of light falls perpendicularly on the flat surface A . Determine the minimum value of the ratio R d for which all light entering the glass through surface A will emerge from the glass through the surface B . The index of refraction of the glass is 1 . 5 .

Step-by-step solution

Consider the representative rays shown in diagram (b). A ray entering the glass through surface A and passing along the inner side of the rod will be reflected by the outer side with the smallest angle α , at which the reflected ray is tangent to the inner side. We have to consider the conditions under which the ray will undergo total internal reflection before reaching B. If α > θ c , the critical angle, at which total internal reflection occurs, all the incident beam will emerge through the surface B. Hence we re