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A plano-convex lens of refractive index 1.5 and radius of curv

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A plano-convex lens of refractive index $1.5$ and radius of curvature $30 cm$ is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object

Name: Video solution 2: A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object
Uploaded: 2023-05-05T07:17:47.000Z
Duration: 7 min
Description: Video solution 2: A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object

20 cm

30 cm

60 cm

80 cm

Views: 5,772 students

Updated on: May 5, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2004

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Alexander Discussed

A plano-convex lens of refractive index

1.5

and radius of curvature

30 cm

is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

A plano-convex lens behaves as a concave mirror, if its one surface (curved) is silvered. The rays refracted from plane surface are reflected from curved surface and again refract from plane surface. Therefore, in this lens two refractions and one reflection occur.
Let the focal length of silvered lens be

F

\frac{1}{F} = \frac{1}{f} + \frac{1}{f} + \frac{1}{f _{m}}

= \frac{2}{f} + \frac{1}{f _{m}}

where,

f =

focal length of lens before silvering,

f_{m} =

focal length of spherical mirror.

\frac{1}{F} = \frac{2}{f} + \frac{2}{R} [∵ R = 2 f_{m}] \dots (i)

Now,

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

Here,

R_{1} = \infty, R_{2} = 30 cm

∴ \frac{1}{f} = (1.5 - 1) (\frac{1}{\infty} - \frac{1}{30})

\frac{1}{f} = - \frac{0.5}{30} = - \frac{1}{60}

f = - 60 cm

Hence, from Eq. (i), we get

\frac{1}{F} = \frac{2}{60} + \frac{2}{30} = \frac{6}{60}

F = 10 cm

Again given that,
Size of object

=

Size of image
i.e.,

O = I

∴ m = - \frac{v}{u} = \frac{I}{O}

\Rightarrow \frac{v}{u} = - 1

v = - u

Thus, from lens formula,

\frac{1}{F} = \frac{1}{v} - \frac{1}{u}

\Rightarrow \frac{1}{10} = \frac{1}{- u} - \frac{1}{u}

∴ \frac{1}{10} = - \frac{2}{u}

∴ = - 20 cm

Hence, to get a real image, object must be placed at a distance 20 cm on the left side of lens

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Question Text	A plano-convex lens of refractive index $1.5$ and radius of curvature $30 cm$ is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object
Updated On	May 5, 2023
Topic	Ray Optics and Optical Instruments
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	491
Avg. Video Duration	6 min

A plano-convex lens of refractive index $1.5$ and radius of curvature $30 cm$ is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object

Text solutionVerified

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A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object

Text solutionVerified

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Questions from JEE Mains 2004 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

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A plano-convex lens of refractive index $1.5$ and radius of curvature $30 cm$ is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object