JEE Main & Advanced Physics Ray Optics Sample Paper Topic Test - Refraction of Light Through Curved Surfaces

Two plano-convex lenses each of focal length 10 cm & refractive index \[\frac{3}{2}\] are placed as shown. In the space left, water \[\left( R.l=\frac{4}{3} \right)\] is filled. The whole arrangement is in air. The optical power of the system is (in diopters)

A) 6.67

B) - 6.67

C) 33.3

D) - 33.3

Correct Answer: A

Solution :

[a]

Focal length of plano-convex lens is 10 cm

\[\frac{1}{10}=\left( \frac{3}{2}-1 \right)\left( \frac{1}{\infty }-\frac{1}{-R} \right)\]

\[\frac{1}{10}=\frac{1}{2}\times \frac{1}{R}\Rightarrow R=5cm\]

Let focal length of water lens is \[{{f}_{w}}\]

\[\frac{1}{{{f}_{w}}}=\left( \frac{4}{3}-1 \right)\left( \frac{1}{-5}-\frac{1}{5} \right)\]

\[\Rightarrow \] \[f=-\frac{15}{2}cm=-\frac{0.15m}{2}=-\frac{3}{40}m\]

Optical powers of system

\[P=\frac{1}{f}+\frac{1}{f}+\frac{1}{{{f}_{w}}}=\frac{1}{0.1}+\frac{1}{0.1}+\left( -\frac{40}{3} \right)=6.67D\]