Question

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 2×108 m/sec, the focal length of the lens is

Answer 1

Here

v = 2×108 ms-1

c = 3×108 ms-1

µ= c/v = 1.5

D = 6 cm = 60 mm

Radius = 30 mm



Here we have to find the radius of the surface of the lens

O is the centre of the circle

So AC is the chord of the circle

By Pythagora’s theorem

R2 = 302 + (R-3)2

=> R2 = 900 + R2 – 6R + 9

=> 909 – 6R  = 0

=> R = 151.5

R1 = 151.5 mm

R2 = ∞ (for plano convex lens one side is a plane)

By lens makers formula

1/f = (µ-1)(1/R1 – 1/R2)

=> 1/f = (1.5 -1) (1/151.5 – 1/∞)

=> 1/f = 0.5×1/151.5

=> 1/f = 1/303

=> f = 303 mm

=> f = 30.3 cm ≈ 30 cm