Question

A thin convex lens made of glass of $\mu =$ 1.5 has refracting surfaces of radii of curvature 10 cm each. The left space of lens contains air and the right space is filled with water of refractive index $\frac{4}{3}$. A parallel beam of light is incident on it. The position of the image is :

• A. $16cm$
• B. $20cm$
• C. $24cm$
• D. $10cm$

Answer 1

Answer: (B)

$20cm$

Data: ${\mu }_a=1,{\mu }_g=1.5,{\mu }_w=1.33,R_1=10cm,R_2=-10cm,u=-\infty$

For left surface,

$\frac{{\mu }_g}{v_1}-\frac{{\mu }_a}{u}=\frac{{\mu }_g-{\mu }_a}{R_1}$

For right surface,

$\frac{{\mu }_w}{v}-\frac{{\mu }_g}{v_1}=\frac{{\mu }_w-{\mu }_g}{R_2}$

From above two,

$\frac{{\mu }_w}{v}-\frac{{\mu }_a}{u}=\frac{{\mu }_g-{\mu }_a}{R_1}+\frac{{\mu }_w-{\mu }_g}{R_2}$

or, $\frac{1.33}{v}=\frac{1.5-1}{10}-\frac{1.33-1}{10}$

$v=\frac{1.33\times 10}{0.66}=20cm$