Question

A convex refracting surface of radius of curvature 15 cm separates two media of refractive indices 4/3 and 1.50. An object is kept in the first medium at a distance of 240 cm from the surface.The position of the image is:

• A. 245 cm
• B. 259 cm
• C. 220 cm
• D. 240 cm

Answer 1

The correct option is B 259 cm

$n_1=\frac{4}{3}=1.33,n_2=1.50$

$u=-240cm,R=15cm$

(convex refracting

gurface)

$\begin{array}{cc}& \frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\\ \Rightarrow & \frac{1.50}{v}-\left(\frac{1.33}{-240}\right)=\frac{150-1.33}{15}\\ \Rightarrow & \frac{1.50}{v}+\frac{1.33}{240}=\frac{0.17}{15}\\ \Rightarrow & \frac{1.50}{2}=\frac{0.17}{15}-\frac{1.33}{240}\\ \Rightarrow & \frac{1.50}{2}=\frac{1.39}{240}\\ \Rightarrow & v=\frac{240\times 1.50}{1.39}=259cm\end{array}$

- Distance of the image from the refracting surface $=259cm$