Question 14: Ray Optics

Question

A spherical interface lens of radius $R$ separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of $4 R$ in front of spherical interface. The magnitude of the magnification of point source image is $\_\_\_\_$ .

Accepted Answer

When light travels from one medium to another through a curved surface, the positions of the object ( $u$ ) and the image (v) are related by the formula:
$$ \frac{\mathrm{n}_2}{\mathrm{v}}-\frac{\mathrm{n}_1}{\mathrm{u}}=\frac{\mathrm{n}_2-\mathrm{n}_1}{\mathrm{R}} $$
Where $\mathrm{n}_1$ is the refractive index of the medium where the object is placed, $\mathrm{n}_2$ is the refractive index of the medium where light enters, R is the radius of curvature.
The refractive index of medium in which object is $\mathrm{n}_1=1$, and that for the image $\mathrm{n}_2=1.4$.
The object distance is $u=-4 R$ (as per sign convention), and radius is $+R$ (convex surface).
$$ \frac{1.4}{v}-\frac{1}{-4 R}=\frac{1.4-1}{R} $$
$$\Rightarrow $$ $\frac{1.4}{v}+\frac{1}{4 R}=\frac{0.4}{R}$
$$\Rightarrow $$ $\frac{1.4}{v}=\frac{0.4}{R}-\frac{0.25}{R}=\frac{0.15}{R}$
$$\Rightarrow $$ $$ \mathrm{v}=\frac{1.4 \mathrm{R}}{0.15}=\frac{140 \mathrm{R}}{15}=\frac{28}{3} \mathrm{R} $$
For a spherical refracting interface, the magnification is given by :
$$ \mathrm{m}=\frac{\mathrm{n}_1 \mathrm{v}}{\mathrm{n}_2 \mathrm{u}} $$
$$\Rightarrow $$ $\mathrm{m}=\frac{1 	imes\left(\frac{28}{3} \mathrm{R}ight)}{1.4 	imes(-4 \mathrm{R})}$
$$\Rightarrow $$ $\mathrm{m}=\frac{28 \mathrm{R} / 3}{-5.6 \mathrm{R}}=\frac{28}{3 	imes(-5.6)}=\frac{28}{-16.8}$
$$\Rightarrow $$ $$ |\mathrm{m}|=\frac{28}{16.8}=1.666 \ldots $$
Therefore, the magnitude of the magnification of point source image is 1.66 .
Thus, the correct option is (A).

Answer

1.66

Answer

2.33

Answer

2.66

Answer

1.33

Ray Optics

A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4 R in front of spherical interface. The magnitude of the magnification of point source image is \_\_\_\_ .

Choose the correct answer: