Question

A diverging meniscus lens of 1.5 refractive index has concave surfaces of radii 3 and 4 cm. The position of image if an object is placed 12 cm infront of the lens is

• A. -24 cm
• B. -8 cm
• C. 8 cm
• D. 24 cm

Answer 1

The correct option is B -8 cm

$\begin{array}{c}\frac{1}{f}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\\ Forgivenconcavelens,R_1=-3cm,R_2=-4cm\\ \frac{1}{v}-\frac{1}{u}=\left(\mu -1\right)\left(\frac{1}{-3}+\frac{1}{4}\right)\\ or,\frac{1}{v}-\frac{1}{\left(-12\right)}=\left(1.5-1\right)\left(\frac{-4+3}{12}\right)\\ or,\frac{1}{v}+\frac{1}{12}=0.5\times \frac{-1}{12}=\frac{-1}{24}\\ or,\frac{1}{v}=-\frac{1}{24}-\frac{1}{12}=\frac{-1-2}{24}=\frac{1}{8}\\ or,v=-8cm\end{array}$

Hence,

option $\left(B\right)$ is correct answer.