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 = 2×10^{8} ms^{-1}

c = 3×10^{8} 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

R^{2} = 30^{2} + (R-3)^{2}

=> R^{2} = 900 + R^{2} – 6R + 9

=> 909 – 6R = 0

=> R = 151.5

R_{1} = 151.5 mm

R_{2} = ∞ (for plano convex lens one side is a plane)

By lens makers formula

1/f = (µ-1)(1/R_{1} – 1/R_{2})

=> 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

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