A glass sphere $(μ = 1.5)$ of radius 8 cm is placed in sunlight. Where is the image of the sun formed by the light passing through the sphere? When refraction by second surface of sphere

4 cm

As the sun is very far away, the incident ray can be assumed as coming from infinity.

For refraction at first surface:

Using $\frac{m_1}{u}+\frac{m_2}{v}=\frac{m_2-m_1}{R}$

$⇒\frac{1}{∞}+\frac{1.5}{v_1}=\frac{1.5-1}{+8}$

$⇒v_1=24cm$

The rays try to converge at $I_1$ and hence for the second surface it is a virtual object. 

For second surface:

$\frac{m_1}{u}+\frac{m_2}{v}=\frac{m_2-m_1}{R}$

$u = –(24 – 16) = –8 cm$

$⇒\frac{1.5}{-8}+\frac{1}{v_2}=\frac{1-1.5}{-8}$

$⇒v_2=4cm$

Hence the final image is formed at $I_2$ which is 4 cm from the other surface of the sphere.