Question

Example 2
A transparent sphere of radius R and refractive index n is kept in 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?​

Answer 1

Explanation:

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

Solution:

Using the equation,

v

μ

2

−

u

μ

1

=

R

μ

2

−μ

1

For the refraction at the first surface of the sphere,

(air to glass)

∞

μ

−

−x

1

=

R

μ−1

, Here x is the distance of point object from the sphere, as shown in above fig.

⟹

x

1

=

R

μ−1

⟹x=

μ−1

R

Hence the object should be placed this distance from the surface of the sphere in order to get real image.