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

Answer

A, D

Explanation

The focal length of lens is given by,
`(1)/(f) = (mu - 1). (1)/(R_1) - (1)/(R_2)`
`rArr (mu - 1) = (1)/(f)xx (1)/((1)/(R_1) - (1)/(R_2))`
`=(k)/(f)….. (i)`
so, `mu_r -1 = (k)/(100) … (ii)`
`mu_y -1 = (k)/(98)…. (ii)`
and `mu_(upsilon) -1 = (k)/(96) ..... (ii)`
So, Dispersive power ` =omega`
`=(mu_(upsilon)j - mu_r)/(mu_y -1)`
`=(mu_(upsilon) -1) - (mu_r -1))/((mu_y -1))`
` =((k)/(96) - (k)/(100))/((k)/(98)) = (98xx 4)/(9600)`
=0.0408