What is the refractive index of material of a plano-convex lens, if the redius of curvature of the convex surface is 10 cm and focal length of the lens is 30 cm ?

Q: What is the refractive index of material of a plano-convex lens, if the redius of curvature of the convex surface is 10 cm and focal length of the lens is 30 cm ?

Sol: According to lens-maker’s formula

$\large \frac{1}{f} = (\mu -1) (\frac{1}{R_1} – \frac{1}{R_2})$

Here f = 30 cm , R1 = 10 cm and R2 = ∞

$\large \frac{1}{30} = (\mu -1) (\frac{1}{10} – \frac{1}{\infty})$

i.e., 3 μ – 3 = 1

or, μ = 4/3