Question

Parallel rays are incident on a solid sphere of the glass of diameter $12cm$. Where will the rays be centralized after refraction finally? Refractive index of glass $=1.5$.

• A. At a distance of $6cm$ in front of the sphere
• B. At a distance of $6cm$ behind the sphere
• C. At a distance of $3cm$ in front of the sphere
• D. At a distance of $3cm$ behind the sphere

Answer 1

Answer: (D)

At a distance of $3cm$ behind the sphere

$\begin{array}{cc}\text{Refraction at}A& \\ \begin{array}{cc}\frac{{\mu }_1}{u}-\frac{{\mu }_2}{V}& =\frac{{\mu }_1-M_2}{R}\\ \frac{1}{\infty }-\frac{1.5}{v}& =\frac{1-1.5}{6}\\ & \frac{1.5}{V}=\frac{0.5}{6}\\ V& =\frac{1.5\times 6}{0.5}\\ V& =18\end{array}& \end{array}$

$\begin{array}{c}\text{Refraction at}B\\ \begin{array}{c}u=18-12=6cm\\ {\mu }_1=1.5\\ V=?\\ {\mu }_2=1\\ R=6cm\\ \frac{{\mu }_1}{u}-\frac{{\mu }_2}{v}=\frac{{\mu }_1-{\mu }_2}{R}\\ \frac{1.5}{6}-\frac{1}{v}=\frac{1\cdot 5-1}{-6}\\ \frac{1.5}{6}+\frac{0.5}{6}=\frac{1}{V}\end{array}\end{array}$

$\begin{array}{cc}\frac{1}{v}& =\frac{2}{6}\\ V& =3m\\ v& =+3cm\\ \text{so parallel rays be centralized.}& \\ \text{at a distance of}3cm\text{behind the}& \\ \text{sphere.}& \end{array}$