Question

A parallel beam of light traveling in water of refractive index 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 C.

• 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

Object is at infinity as a parallel beam of light falls on the spherical surface. Using formula:
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}\text{Where}{\mu }_2=\text{R.I of air inside bubble = 1}{\mu }_1=\text{R.I of water from where incident rays are coming}=\frac{4}{3}R=2mmu=\text{infinity}\frac{1}{v_1}-\frac{4/3}{\infty }=\frac{1-4/3}{2}{v}_1=-6mm\text{The first surface will form a virtual}\text{image at a distance 6 mm to the left of}\text{the first surface.}\text{This virtual object is in air (as rays}\text{are incient on the second surface}\text{coming from within the bubble.}u=\text{Virtual object distance from}\text{second surface =}-(6+2R)=-(6+4)=-10mm\text{Using sign conventions R=-2 mm}\text{for the second surface}\frac{4/3}{v_2}=\frac{1}{(-2)}{v}_2=-5mm$
The final image I2 is formed at a distance of 5mm to the left of the second surface. The final image is at a distance of 5 -4 = 1mm to the left of the first surface and 3mm to the left of centre, as shown in figure.