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 ?

Explanation

Here, `AB = 6 cm, DO = 3mm = 0.3 cm, v = 2 xx 10^(8) m//s, f = ?`
From the geometry of the circle, Fig.
`AD xx DB = OD xx DE = (OE -OD)`
or `(6)/(2) xx (6)/(2) = 0.3 (2 R_(1) - 0.3)`,
where `R_(1)` is radius of spherical surface
`9 = 0.6 R_(1)` (Neglecting `0.3 cm` compared to `2 R_(1)`)
`R_(1) = (9)/(0.6) = 15 cm`.
As `mu = ( c)/(v) :. mu = (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)/(15) - (1)/(oo)) = (1)/(30)` (`becasue` `R_(2) = oo` for plane surface)
`:. f = 30 cm`