please answer!!

Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3mm. If speed of light in material of

lens is 2 x 10^8 m/s, the focal length of the lens is :

(1) 15 cm (2) 20 cm (3) 30 cm (4) 10 cm

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