JEE Main 2019 · Physics · Ray and Wave Optics · medium

A biconvex thin lens made of glass of refractive index 1.5 has radii of curvature 20 cm and 30 cm. When the lens is completely immersed in a liquid…

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A biconvex thin lens made of glass of refractive index

1.5

has radii of curvature

20\ \mathrm{cm}

and

30\ \mathrm{cm}

. When the lens is completely immersed in a liquid of refractive index

1.6

, its focal length is

Show answer and solution

Answer: (B) $-192\ \mathrm{cm}$ (diverging)

Use the lens maker's formula with the relative refractive index

\mu_{rel}=1.5/1.6

\dfrac1f=\left(\mu_{rel}-1\right)\left(\dfrac1{R_1}-\dfrac1{R_2}\right)

with

R_1=+20

and

R_2=-30\ \mathrm{cm}

for a biconvex lens. Here

\mu_{rel}-1 = -\tfrac1{16}

and

\tfrac1{20}+\tfrac1{30}=\tfrac1{12}

, so

\dfrac1f=-\dfrac1{192}

and

f=-192\ \mathrm{cm}

. The lens, convergent in air with

f=24\ \mathrm{cm}

, becomes divergent because the liquid is optically denser than the glass.

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