A plano - convex lens has diameter 5 cm and its thickness at the centre is 0.25 cm . If the speed of light inside the lens is `2xx10^(8)ms^(-1)`, then what is the focal length (in cm) of the lens?

Answer

`25.25`

Explanation

R. I. of lens,
`mu = c/v = (3 xx 10^(8))/(2 xx 10^(8)) = 3/2`
From `DeltaACO`, radius of curvature of lens is,
`R^(2) = R_(1)^(2) + (R-0.25)^(2)`
`therefore R^(2) = (2.5)^(2) + (R-0.25)^(2)`
`therefore 0.5 R = 6.3125`
`therefore R =12.625 cm`
`F = R/(mu-1) = (12.625)/(3/2-1) = 25.25` cm