Physics - Geometrical Optics Question with Solution | TestHub

Refraction at plane surface (1), $n_1=1,n_2=1.5=\frac{3}{2},u=-mR,v=?$ Using formula, $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$ $\begin{array}{rl}& \because R=\infty \text{ for plane surface. }\\ & \because \frac{3/2}{v}-\frac{1}{(-mR)}=0\\ & \therefore v=-\frac{3}{2}mR\end{array}$ Refraction at spherical surface (2) $\begin{array}{rl}& u=-\left(\frac{3}{2}mR+R\right)\text{ and }R=-R,v=\infty ,\\ & n_1=\frac{3}{2},n_2=1\end{array}$ $\frac{1}{\infty }-\frac{3/2}{\left[-\left(\frac{3}{2}mR+R\right)\right]}=\frac{1-3/2}{-R}$ $\begin{array}{rl}& \Rightarrow \frac{3/2}{\frac{R(3m+2)}{2}}=\frac{1/2}{R}\\ & \Rightarrow \frac{6}{3m+2}=1\Rightarrow 3m+2=6\\ & m=\frac{4}{3}\\ & \end{array}$