question_answer 64)

  The mixture of a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions « vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance d « h, the height of the column.

Answer:

                  In Fig. 6(EP).15, we have shown a ray of light entering the coumn at (x, y) at 90° to the vertical. A portion of ray between x and  deviates through an angle dQ, emerging at  at angle ,                 While the angle at the entry is                 According to Snell?s law,                                                 As  is small,  and sin                         (fourth term is negligibly small)                                                 From Fig. 6(EP). 15,   or                                                   This is the required deviation in travelling a horizontal distance d.