JEE Main · 2014 · 06 Apr 2014 · Offline · Geometrical Optics

A thin convex lens made from crown glass

(μ = \frac{3}{2})

has focal length f. When it is measured in two different liquids having refractive indices

\frac{4}{3}

and

\frac{5}{3}

, it has the focal lengths

f_{1}

and

f_{2}

respectively. The correct relation between the focal lengths is:

Answer: (D)

Solution

Use the lens-maker's formula with the surrounding medium folded in:

\frac{f _{m}}{f} = \frac{μ - 1}{\frac{μ}{μ _{m}} - 1}

. In the first liquid,

μ_{m} = \frac{4}{3}

, so

\frac{f _{1}}{f} = \frac{1/2}{( 3/2 ) / ( 4/3 ) - 1} = \frac{1/2}{1/8} = 4

, giving

f_{1} = 4 f

, larger than

f

and still positive. In the second liquid,

μ_{m} = \frac{5}{3}

, so

\frac{f _{2}}{f} = \frac{1/2}{( 3/2 ) / ( 5/3 ) - 1} = \frac{1/2}{- 1/10} = - 5

, so

f_{2}

comes out negative, the converging lens having turned diverging. Thus

f_{1} > f

while

f_{2}

becomes negative.

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option