In an experiment,a convex lens of focal lengt | vedclass

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Question

(A) Given: Focal length of the lens $f_l = 15 \, cm$,object distance $u = -20 \, cm$.Using the lens formula,$\frac{1}{f_l} = \frac{1}{v} - \frac{1}{u}

Vedclass · Accepted Answer

$27.5$

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(A) Given: Focal length of the lens $f_l = 15 \, cm$,object distance $u = -20 \, cm$.Using the lens formula,$\frac{1}{f_l} = \frac{1}{v} - \frac{1}{u}$.$\frac{1}{v} = \frac{1}{15} - \frac{1}{20} = \frac{4-3}{60} = \frac{1}{60}$.So,$v = 60 \, cm$. The image is formed $60 \, cm$ to the right of the lens.For the object and image to coincide,the rays must strike the convex mirror normally. This happens if the rays are directed towards the center of curvature $(C)$ of the convex mirror.The distance of the mirror from the lens is $d = 5 \, cm$. The distance of the center of curvature from the mirror is $R = 2f_m$.The image formed by the lens is at a distance of $60 \, cm$ from the lens. Since the mirror is $5 \, cm$ from the lens,the distance of the image from the mirror is $60 - 5 = 55 \, cm$.Thus,the radius of curvature $R = 55 \, cm$.Since $R = 2f_m$,the focal length of the convex mirror is $f_m = \frac{R}{2} = \frac{55}{2} = 27.5 \, cm$.

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