Question

a plano-convex lens of glass has radius of curvature of 30 cm if the glass has refractive index of 1.7 find the focal length of lens

Answer 1

Given that the lens is a plano-convex lens. Thus, radius of both the spherical surfaces will be equal. If r₁ and r₂ are the radius of the two surfaces, then

r₁ = r₂ = 30 cm [Given, radius of curvature = 30 cm]

Also, Refractive index of the glass, μ = 1.7

Now, using Lens Maker's formula:

$\frac{1}{f} = (n - 1)(\frac{1}{r_1} - \frac{1}{r_2})$

= (1.7 - 1)(2/r₁) [As r₁ = r₂]

= 0.7 x 2/r₁

= 1.4/r₁

Thus, f = r₁/1.4 = 30/1.4 = 21.42 cm

Hence the focal length of the lens is 21.42 cm.