#### Question

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

#### Solution

Here, filament of the lamp acts as an object.

v = Image distance

and u = Object distance

According to the question:

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

and magnification m = v/u = 3

or, v = 3 u

or, v-3u = 0 ...(ii)

Solving (i) and (ii), we get:

u = 20 cm

For the focal length of the lens, we have:

Distance of lens from the filament, u = -20 cm

`v=3xxu=3xx20=60`cm

Applying lens formula, we get:

1/v -1/u = 1/f

1/60 + 1/20 = 1/f

(1+3)/60= 1/f

1/f=4/60

f=15 cm

So, focal length f = 15 cm

Is there an error in this question or solution?

Solution The Filament of a Lamp is 80 Cm from a Screen and a Converging Lens Forms an Image of It on a Screen, Magnified Three Times. Find the Distance of the Lens from the Filament and the Foca Concept: Mirror Formula and Magnification.