A planoconvex lens becomes an optical system of 28 cm focal length… | JEE Main 2018 (15 Apr, Shift 1)

Q64JEE Main 2018 · 15 APR · SHIFT 1Medium

Combination of Lenses

A planoconvex lens becomes an optical system of $28\text{ cm}$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.

If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig- B, it acts like an optical system of focal length $10\text{ cm.}$ The refractive index of the material of lens is:

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Answer: (b)

Fig A (plane face silvered): $F_A = \frac{f_L}{2} = 28 \Rightarrow f_L = 56\text{ cm}$ , and $f_L = \frac{R}{\mu-1}$ .
Fig B (curved face silvered, light enters plane face): plane face has no power, so the system is a concave mirror inside glass, $F_B = \frac{R}{2\mu} = 10 \Rightarrow R = 20\mu$ .
$\frac{20\mu}{\mu-1} = 56 \Rightarrow 36\mu = 56 \Rightarrow \mu = 1.555$
So the answer is (b) 1.55.

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Combination of Lenses question from JEE Main 2018 (15 Apr, Shift 1)

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