The diameter of a plano convex lens is `6 cm` and thickness at the centre is `3 mm`. If the speed of light in the material of the lens is `2 xx 10^8 m//s`, what is the focal length of the lens ?

Options

A. `15 cm`
B. `20 cm`
C. `30 cm`
D. `10cm`

Answer

C

Explanation

Here, `d = 6 cm, h = 3 mm = 0.3 cm`,
`v = 2 xx 10^(8)m//s, f = ?`
If `R` is radius of curvature of the convex surface of lens, then from
`((d)/(2))^(2) = (2 R - h)h = 2 R h` `(because h lt lt R)`
`R = (d^(2)//4)/(2h) = (6^(2)//4)/(2 xx 0.3) = 15 cm`
`mu = ( c)/(v) = (3 xx 10^(8))/(2 xx 10^(8)) = (3)/(2)`
From `(1)/(f) = (mu - 1)((1)/(R_(1)) - (1)/(R_(2)))`
`= ((3)/(2) - 1)((1)/(oo) + (1)/(15)) = (1)/(30)`
`f = 30 cm`