JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Geometrical Optics

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

2 \times 1 0^{8} ms^{- 1}

. The focal length of the lens is:

Answer: (C)

Solution

The refractive index follows from the speed of light inside the material:

n = \frac{c}{v} = \frac{3 \times 1 0 ^{8}}{2 \times 1 0 ^{8}} = 1.5

The curved face is a spherical cap of height

t = 3 mm = 0.3

cm standing on a circle of radius

r = 3

cm, for which

r^{2} = t (2 R - t)

. Since

t

is small beside

R

R \approx \frac{r ^{2}}{2 t} = \frac{9}{0.6} = 15 cm

The plane face has infinite radius and drops out of the lens maker's formula, so

\frac{1}{f} = (n - 1) \frac{1}{R} = \frac{0.5}{15}

The focal length of the lens is

30

cm.

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option