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Q.

A transparent sphere of radius R and refractive index $μ$ is kept in the air. At what distance from the surface of the sphere should a point object be placed on the principal axis so as to form a real image at the same distance from the second surface of the sphere?

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a

b

c

d

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answer is C.(Unlock A.I Detailed Solution for FREE)

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Detailed Solution

Concept- By maintaining the point object at a specific distance from the sphere's first surface in order to acquire its image at infinity (since the image is real) from the second surface, we may make a ray diagram.Given: A transparent sphere of radius

R

and refractive index

μ

is kept in the air.
To find the distance from the surface of the sphere where a point should be placed so as to form a real image at the same distance from the other side of the sphere
Using the equation,

μ 2 v − μ 1 u = μ 2 − μ 1 R

For the refraction at the first surface of the sphere,
(air to glass)

μ ∞ − 1 − x = μ − 1 R

, Here

x

is the distance of a point object from the sphere, as shown in above fig.
Question Image

Question Image

⇒ 1 x = μ − 1 R ⇒ x = R μ − 1

Hence, the object should be placed this distance from the surface of the sphere in order to get a real image.
Hence, option 3 is correct.

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