Question

A glass refractive index 1.5 and radius 10 cm,has a spherical cavity of radius 5 cm concentric with it. A narrow beam of parallel light is directed into the sphere.Find the final image and its nature.

• A. -25 cm left of $S_1$, virtual
• B. 25 cm right of $S_4$, real
• C. 15 cm left of $S_4$, virtual
• D. 20 cm right of $S_4$, virtual

Answer 1

The correct option is A -25 cm left of $S_1$, virtual

$\begin{array}{c}Ateachofthesurface,\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}istobeused.\\ At{S}_1\\ \frac{1.5}{v_1}-\frac{1}{\left(-\infty \right)}=\frac{0.5}{10}\\ v_1=30cm\\ Thereforeat{S}_2.u_2=+25cm\\ \frac{1}{v_2}-\frac{1.5}{25}=\frac{-0.5}{5}\\ v_2=025cm\\ Followingthe\log icpreviouslyused,u_3=-\left(25+10\right)=-35cm\\ At{S}_3,\\ \frac{1.5}{v_3}-\frac{1}{-35}=\frac{-0.5}{5}\\ v_3=\frac{-35}{3}cm\\ Thismakes{u}_4=\frac{-50}{5}\\ v_3=\frac{1.5}{\frac{-50}{3}}c=\frac{-0.5}{-10}\\ Therefore{v}_4\\ =-25cm\\ Sincetheimagelieslefttothepointofinitialincidence\left(S_1\right),theimageisvirtual.\end{array}$