Question

Two plano concave lenses (1 and 2) of glass of refractive index $1.5$ have radii of curvature $20cm$ and $30cm$. They are placed in contact with their curved surface towards each other and the space between them is filled with liquid of refractive index $\frac{4}{3}$.Then the combination is:

• A. convex lens of focal length $60$cm
• B. concave lens of focal length $72$cm
• C. concave lens of focal length $66.6$cm
• D. convex lens of focal length $66.6$cm

Answer 1

The correct option is A convex lens of focal length $60$cm

$\begin{array}{c}{}_a{\mu }_g=1\cdot 5\\ {}_a{\mu }_L=\frac{4}{3}{\Rightarrow }_L\mu a=\frac{3}{4}\\ R_1=20cm\\ R_2=30cm\end{array}$

$\begin{array}{c}\text{Using Lens Maker's formula}\\ \frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})\\ \frac{1}{f}=(\frac{3\times 4}{2\times 3}-1)(\frac{1}{20}-\frac{1}{30})\\ \frac{1}{5}=\left(1\right)\left(\frac{3-2}{60}\right)\\ f=60m\\ \text{Lens is convex}\end{array}$