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A lens of focal length 20 cm forms the image of a bright object kept 30 cm from it on a screen. If the lens is replaced by another lens, the object has to be moved by 5 cm to obtain a sharp image on the screen. Find the possible values of the focal length of the second lens.
Asked by k.suman39 | 19 Apr, 2019, 09:08: AM
Initially the object is placed at 30 cm from the lens. As the image is formed on screen, it is real image. Thus, the lens is convex lens.
The focal length of this lens is 20 cm.
Thus,
f = + 20 cm
u = - 30 cm

Using lens formula,

Thus, bright and sharp image is formed on screen at 60 cm to the right of the lens.
Thus, screen is placed at 60 cm.

Now, the lens is replaced and the object is moved either 5 cm towards the lens or away from the lens.

In case, when the object is moved towards the lens,
u = - 25 cm
f = ?
v = + 60 cm

Thus, using lens formula,

In case, when the object is moved 5 cm away from the initial position from the lens,
u = - 35 cm
v = +60 cm
f = ?

Again using the lens formula,

Thus, two possible values of focal length of lens are 17.6 cm and 22.10 cm
Answered by Shiwani Sawant | 19 Apr, 2019, 11:56: AM

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