Ray Optics

JEE Main level, single correct, medium

213 of 295

Question 213 of 295

A plane convex lens of refractive index 1.51.5 and radius of curvature 30 cm30 \mathrm{~cm} is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object?

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Answer: (A) 20 cm20 \mathrm{~cm}

1F=2f1+1fm and 1f1=(1.5−1)(1∞−1−30)=160 and fm=15 cm.∴F=10 cm.\begin{aligned} & \frac{1}{F}=\frac{2}{f_1}+\frac{1}{f_m} \\ & \text { and } \frac{1}{f_1}=(1.5-1)\left(\frac{1}{\infty}-\frac{1}{-30}\right)=\frac{1}{60} \\ & \text { and } f_m=15 \mathrm{~cm} . \\ & \therefore F=10 \mathrm{~cm} . \end{aligned}
Object should be placed at 20 cm20 \mathrm{~cm} from the lens.

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