Pls explain in detail asap

Dear Student,

Given,

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

\frac{1}{f} = (µ - 1) (\frac{1}{R 1} - \frac{1}{R 2}) = > \frac{1}{f} = (1.5 - 1) (\frac{1}{151.5} - \frac{1}{\infty}) = > \frac{1}{f} = 0.5 \times \frac{1}{151.5} = > \frac{1}{f} = \frac{1}{303}

=> f = 303 mm

=> f = 30.3 cm ≈ 30 cm
Thus, Correct Option (3)

Regards