Question

A parallel beam of light travelling in water $(\mu =4/3)$ is refracted by a spherical bubble of radius $R=2mm$. Assuming the light rays to be paraxial, find the position of the final image from the centre.

• A. $2mm$ to the left
• B. $3mm$ to the left
• C. $5mm$ to the right
• D. $8mm$ to the left

Answer 1

The correct option is B $3mm$ to the left

For the spherical surface refraction

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=({\mu }_2-{\mu }_1)/R$

$P_1=$First surface

${\mu }_1=\frac{4}{3}$

${\mu }_2=1$

$R=0.2$cm

$u_1=\infty$

$\frac{1}{v_1}-\frac{4/3}{\infty }=\frac{1-4/3}{0.2}$

$\therefore v_1=0.6$cm

The $1^{st}$ surface will form a virtual img at $0.6$

${\mu }_1=1$

${\mu }_2=\frac{4}{3}$

$R=-0.2$

$u_2=-(0.6+0.4)=-1.0$cm

$\frac{4/3}{v_2}-\frac{1}{(-1)}=\frac{4/3-1}{-0.2}$

$v_2=0.5$cm

The image will be formed at $0.3$cm from the center or $3$mm to the left.