JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Geometrical Optics

The graph shows how the magnification m produced by a thin lens varies with image distance

v

. What is the focal length of the lens used?

(A) $\frac{b ^{2}}{a c}$
(B) $\frac{a}{c}$
(C) $\frac{b ^{2} c}{a}$
(D) $\frac{b}{c}$ ✓ Correct

Answer: (D)

Solution

For a thin lens the magnification is

m = \frac{v}{u}

, and combining this with

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

eliminates

u

to give

m = 1 - \frac{v}{f}

. So a plot of

m

against the image distance

v

is a straight line whose slope is

- \frac{1}{f}

. Reading the slope off the graph as the ratio of the marked intercepts, the focal length comes out as

f = \frac{b}{c}

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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