(a) Monochromatic light of wevelengh 589 nm in incident from air on a water surface. If
`mu` for water is 1.33, find the wevelength, frequency and speed of the refracted light .
(b) A duble conbex lens is made of a glass of refractive index 1.55 , with both faces of the
same radius of curbature. Find the radius of curvature required , if the focal length is 20 cm.

Explanation

Given, `lambda = 589xx10^(-9)m`
As ` mu alpha (1)/(lambda)`
` therefore (mu_(1))/(mu_(2)) = (lambda_(2))/(lambda_(1)) = rArr lambda_(2) = (lambda_(1) mu_(1))/(mu_(2))`
`rArr lambda_(2) = (589xx1)/(4//3) rArr lambda_(2) = 441.75 `nm
Frequency of the light is independent of the medium.
Speed of refractive light `V_("water") =(C)/(amu_(omega)) =(3xx10^(8))/(1.33) =(2.26xx10^(8))/(m//s)`
(b) Given, `mu = 1.55, f = 20 cm`
Now, `(1)/(f) = (mu -1) ((1)/(R_(1) ) - (1)/(R_(2))) rArr (1)/(20) = (1.55-1) ((1)/(R) + (1)/(R))`
`(1)/(20) = 55xx(2)/(R) rArr R = 20 xx1.1 rArr R = 22 ` cm.