For red, yellow, and violet rays, the focal lengths of a convex lens are 100 cm , 98 cm , and 96 cm respectively. Determine the dispersive power of the material of the lens.

Step-by-step solution

Using the lens maker's formula, the focal length f is related to the refractive index by: 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) Let K = ( 1 R₁ - 1 R₂ ) . The refractive indices for violet, red, and yellow light can be written as: _v - 1 = 1 K f_v _r - 1 = 1 K f_r _y - 1 = 1 K f_y The dispersive power of the material is given by: = _v - _r _y - 1 = ( _v - 1) - ( _r - 1) _y - 1 Substituting the expressions for the refractive indices: = 1 K f_v - 1 K f_r 1 K f_y = 1 f_v - 1 f_r 1 f_y = f_r - f_v f_r f_v f_y Given f_r = 100 cm