Question

Calculate the value of refractive index $\left(\mu \right)$ for given situation

• A. $\mu =1.5$
• B. $\mu =2$
• C. $\mu =0.5$
• D. $\mu =3$

Answer 1

The correct option is B $\mu =2$

From the figure,

The focal length can be obtained as $f=r$

The object distance is $u=\infty$

The image distance is $v=2r$

Apply the lens formula

$\frac{\left({\mu }_g-{\mu }_a\right)}{f}=\frac{{\mu }_g}{v}+\frac{{\mu }_a}{u}$

The refractive index of air is ${\mu }_a=1$

$\frac{\left({\mu }_g-1\right)}{r}=\frac{{\mu }_g}{2r}+\frac{1}{\infty }$

$\frac{\left({\mu }_g-1\right)}{r}=\frac{{\mu }_g}{2r}$

${\mu }_g=2\left({\mu }_g-1\right)$

$\therefore {\mu }_g=2$

Hence the refractive index of the given medium is $\mu =2$ .