Question

A glass sphere, refractive index $1.5$ and radius $10cm$, has a spherical cavity of radius $5cm$ concentric with it. A narrow beam of parallel light is directed into the sphere. Find the final image and its nature.

• A. $25cm$ left of $S_4$, virtual
• B. $25cm$ right of $S_4$, virtual
• C. $15cm$ left of $S_4$, virtual
• D. $20cm$ right of $S_4$, virtual

Answer 1

Answer: (A)

$25cm$ left of $S_4$, virtual

We will have single surface refractions successively at the four surfaces $S_1,S_2,S_3$, and $S_4$. Do not forget to shift origin to the vertex of respective surface.
Refractive at first surface $S_1$: Light travels from air to glass.
$\frac{1.5}{v_1}-\frac{1}{\infty }=\frac{(1.5-1)}{(+10)}$
$v_1=30cm$
First image is object for the refraction at second surface.
For refraction at surface $S_2$: Light travels from glass to air
$\frac{1}{v_2}-\frac{1.5}{+\left(25\right)}=\frac{1-1.5}{(+5)}$
$v_2=-25cm$
For refraction at surface $S_3$: Light travels from air to glass.
$\frac{1.5}{v_3}-\frac{1}{(-35)}=\frac{(1.5-1)}{(-5)}$
$v_3=-35/3cm$
For refraction at surface $S_4$: Light travels from glass at air
$\frac{1}{v_4}-\frac{1.5}{-(35/3+5)}=\frac{1-1.5}{-10}$
$v_4=-25cm$
The final image is virtual, formed at $25cm$ to the left of the vertex of surface $S_4$.