Question

The filament of a lamp is 80cm from a screen and a converging lens forms an image of it on screen magnified three times. find the distance of the lens from the filament and the focal length of the lens ​

Answer 1

Here, the filament of the lamp acts as an object.

Now,

v = image distance from lens

u = object distance

According to the question,

v + u = 80 (considering magnitude only)...(i)

And, magnification (m) = v/u = 3

=> v = 3u

=> v-3u = 0...(ii)

Solving (i) and (ii)—

u = 20 cm.

For the focal length of the lens,

u = -20 cm

v = 3 × u = 3 × 20 = 60 cm

Using lens formula, i.e. 1/v - 1/u = 1/f

So, 1/60+1/20 = 1/f

Therefore, f = 15 cm

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