Optics 3 Question 7

7. An object is at a distance of 20m from a convex lens of focal length 0.3m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5m/s, the speed and direction of the image will be

(2019 Main, 11 Jan I)

(a) 3.22×103m/s towards the lens

(b) 0.92×103m/s away from the lens

(c) 2.26×103m/s away from the lens

(d) 1.16×103m/s towards the lens

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Answer:

Correct Answer: 7. (d)

Solution:

  1. Lens formula is given as

1f=1v1u1v=1f+1uufu+f=vvu=fu+f

Now, by differentiating Eq. (i), we get

0=1v2dvdt+1u2dudt

[f (focal length of a lens is constant)]

 or dvdt=v2u2du/dtdvdt=fu+fdudt

[using Eq. (ii)]

Given, f=0.3m,u=20m,du/dt=5m/s

dvdt=0.30.3202×5=31972×5=1.16×103m/s

Thus, the image is moved with a speed of 1.16×103m/s towards the lens.



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