JEE Main · 2013 · 07 Apr 2013 · Offline · Geometrical Optics

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

2 \times 1 0^{8} m / s

, the focal length of the lens is :

(A)20 cm
(B)30 cm✓ Correct
(C)10 cm
(D)15 cm

Answer: (B)

Solution

The speed of light in the glass fixes its index,

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

. For the convex cap the sagitta relation

r^{2} \approx 2 R t

links the aperture radius

r = 3 cm

, half the

6 cm

diameter, and the central thickness

t = 0.3 cm

to the radius of curvature:

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

. The lens-maker's formula for a plano-convex lens,

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

, then gives

f = 30 cm

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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