(B) The power of the silvered lens system is given by $P = 2P_L + P_M$,where $P_L$ is the power of the lens and $P_M$ is the power of the mirror.For a

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(B) The power of the silvered lens system is given by $P = 2P_L + P_M$,where $P_L$ is the power of the lens and $P_M$ is the power of the mirror.For a plano-convex lens,the power $P_L = \frac{1}{f_L} = (\mu_g/\mu_l - 1)(1/R_1 - 1/R_2)$.Here,$\mu_g = 1.5$,$\mu_l = 1.2$,$R_1 = R$,and $R_2 = \infty$.So,$P_L = (1.5/1.2 - 1)(1/R - 0) = (1.25 - 1)/R = 0.25/R$.The mirror is the plane surface,so its power $P_M = -1/f_M$. Since it is a plane mirror,$f_M = \infty$,so $P_M = 0$.The effective focal length $F$ of the system is given by $1/F = -(2P_L + P_M)$.Given $F = -0.2 \ m$ (concave mirror),so $1/(-0.2) = -(2 \times (0.25/R) + 0)$.$-5 = -0.5/R$.$R = 0.5/5 = 0.1 \ m$.

Class 12 Physics Ray Optics and Optical Instruments Combination of Lens and Mirror and Silvering of Lens, Cutting of Mirror

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$A$ thin plano-convex lens made of glass of refractive index $1.5$ is immersed in a liquid of refractive index $1.2$. When the plane side of the lens is silver-coated for complete reflection,the lens immersed in the liquid behaves like a concave mirror of focal length $0.2 \ m$. The radius of curvature of the curved surface of the lens is: (in $m$)

JEE MAIN 2025 All JEE MAIN

A
$0.15$
B
$0.10$
C
$0.20$
D
$0.25$

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Class 12

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Ray Optics and Optical Instruments

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Combination of Lens and Mirror and Silvering of Lens, Cutting of Mirror

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$A$ concave mirror of focal length $f_1$ is placed at a distance of $d$ from a convex lens of focal length $f_2$. $A$ beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance $d$ must equal:

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$A$ glass slab of thickness $6 \, cm$ is silvered at one surface. An object is placed at a distance of $8 \, cm$ from the first surface. The image is formed at a distance of $12 \, cm$ behind the silvered surface. Find the refractive index of the glass.

Difficult

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$A$ plano-convex lens made of material of refractive index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object,so that the image coincides with the object?

DifficultKVPY 2009

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Given a thin convex lens (refractive index $\mu_2$),kept in a liquid (refractive index $\mu_1, \mu_1 < \mu_2$) having radii of curvature $|R_1|$ and $|R_2|$. Its second surface is silver-polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

DifficultJEE MAIN 2025

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$A$ luminous object is placed at a distance of $30 \,cm$ from a convex lens of focal length $20 \,cm$. On the other side of the lens,at what distance from the lens should a convex mirror of radius of curvature $10 \,cm$ be placed in order to have an upright image of the object coincident with it (in $,cm$)?

MediumAIPMT 1998

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$A$ concave mirror of focal length $f_1$ is placed at a distance of $d$ from a convex lens of focal length $f_2$. $A$ beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance $d$ must equal:

$A$ glass slab of thickness $6 \, cm$ is silvered at one surface. An object is placed at a distance of $8 \, cm$ from the first surface. The image is formed at a distance of $12 \, cm$ behind the silvered surface. Find the refractive index of the glass.

$A$ plano-convex lens made of material of refractive index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object,so that the image coincides with the object?

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