JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Geometrical Optics

A thin lens made of glass (refractive index

= 1.5

) of focal length

f = 16 cm

is immersed in a liquid of refractive index 1.42. If its focal length in liquid is

f_{ℓ}

, then the ratio

f_{ℓ} / f

is closest to the integer:

(A)17
(B)1
(C)9✓ Correct
(D)5

Answer: (C)

Solution

In air the lens obeys

\frac{1}{f} = (μ_{g} - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})

, and in the liquid the factor out front becomes

(\frac{μ _{g}}{μ _{ℓ}} - 1)

. Their ratio cancels the radii:

\frac{f _{ℓ}}{f} = \frac{μ _{g} - 1}{\frac{μ _{g}}{μ _{ℓ}} - 1} = \frac{0.5}{\frac{1.5}{1.42} - 1} = \frac{0.5}{0.0563} \approx 8.9

, which rounds to the integer

9

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option

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