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  4. Behind a thin converging lens having both the surfaces of the same radius 10 cm, a plane mirror has been placed. The image of an object at a distance of 40 cm from the lens is formed at the same position. What is the refractive index of the lens?

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Q. Behind a thin converging lens having both the surfaces of the same radius $10\, cm$, a plane mirror has been placed. The image of an object at a distance of $40\, cm$ from the lens is formed at the same position. What is the refractive index of the lens?Physics Question Image

Ray Optics and Optical Instruments

Solution:

" $O$ " act as the focal point.
Also, $ \frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) $
$\Rightarrow \frac{1}{40}=(\mu-1)\left(\frac{1}{10}+\frac{1}{10}\right) $
$ \frac{1}{40}=(\mu-1)\left(\frac{2}{10}\right)$
$\Rightarrow \mu=9 / 8$

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