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
Answer & explanation
Correct answer: option 1
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.