Ray Optics

JEE Main level, single correct, medium

197 of 295

Question 197 of 295

An object is at a distance of 20 m20 \mathrm{~m} from a convex lens of focal length 0.3 m0.3 \mathrm{~m}. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s5 \mathrm{~m} / \mathrm{s} the speed and direction of the image will be

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Answer: (D) 1.16×10−3 m/s1.16 \times 10^{-3} \mathrm{~m} / \mathrm{s} towards the lens

Bylens formula

1v−1u=1f1v−1(−20)=1031v=103−1201v=19760;v=60197\begin{array}{l} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \frac{1}{v}-\frac{1}{(-20)}=\frac{10}{3} \\ \frac{1}{v}=\frac{10}{3}-\frac{1}{20} \\ \frac{1}{v}=\frac{197}{60} ; \quad v=\frac{60}{197} \end{array}

Magnification of lens (m) is given by

m=(vu)=(60197)20\mathrm{m}=\left(\frac{\mathrm{v}}{\mathrm{u}}\right)=\frac{\left(\frac{60}{197}\right)}{20}

velocity of image wrt. to lens is given by

vJ/L=m2vO/L\mathrm{v}_{\mathrm{J} / \mathrm{L}}=\mathrm{m}^{2} \mathrm{v}_{\mathrm{O} / \mathrm{L}}

direction of velocity of image is same as that of object

vO/L=5 m/svI/L=(60×1197×20)2\begin{array}{l} \mathrm{v}_{\mathrm{O} / \mathrm{L}}=5 \mathrm{~m} / \mathrm{s} \\ \mathrm{v}_{\mathrm{I} / \mathrm{L}}=\left(\frac{60 \times 1}{197 \times 20}\right)^{2} \end{array}

=1.16×10−3 m/s=1.16 \times 10^{-3} \mathrm{~m} / \mathrm{s} towards the lens

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