Question

An object is placed at a distance of $20Cm$, in rarer medium, from the pole ofa convex spherical refracting surface of radius of curvature $10Cm$. If the refractive index of the rarer medium is $1$ and of the refracting medium is $2$, then the position of the image is at:

• A. $\left(40/3\right)$ cm from the pole and inside the denser medium.
• B. $40$ cm from the pole and inside the denser medium.
• C. $\left(40/3\right)$ cm from the pole and outside the denser medium.
• D. $40$ cm from the pole and outside the denser medium.

Answer 1

The correct option is B $40$ cm from the pole and inside the denser medium.

$R=+10,u=-20cm{\mu }_1=1cm{\mu }_2=1.5cm$

We know

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

$\frac{2}{v}=\left[\frac{\left(1\right)}{-20}\right]=\frac{2-1}{10}$

$\frac{2}{v}=\frac{1}{10}-\frac{1}{20}$

$\frac{2}{v}=\frac{1}{20}$

$v=40cm$