If the focal length of a lens for red and violet light rays respectively are `f_R` and `f_V` then which of the following is true relationship ?

Options

A. `f_R ge f_V`
B. `f_R gt f_V`
C. `f_R = f_V`
D. `f_R le f_V`

Answer

B

Explanation

`1/f=(n-1)[(1)/(R_1)-(1)/(R_2)]`
`therefore(1)/(f_R)=(n_R-1)((1)/(R_1)-(1)/(R_2))` and
`(1)/(f_V)=(n_V-1)((1)/(R_1)-(1)/(R_2))`
`therefore" Ratio "(f_V)/(f_R)=(n_R-1)/(n_V-1)`
`n_R lt n_V`
`therefore n_R-1 lt n_V-1`
`therefore (n_R-1)/(n_V-1) lt 1`
`therefore (f_V)/(f_R) lt 1`
`therefore f_V lt f_R`
`therefore f_R gt f_V`