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.

Answer 1

Given:

The distance of the filament from the screen is 80 cm

The lens is converging, which is a convex lens.

magnification (m) = 3

The focal length of the convex lens is

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

v = image distance from lens

u = object distance

According to the question, v + u = 80 ( taking only magnitude )    ...(i)

and magnification `m = v/u = 3`

Or,

⇒ v = 3u    ...(ii)

Solving (i) and (ii),

we get u = 20 cm.

For finding the focal length, we have to apply the sign convention.

So, u = −20 cm

As we have found out

v = 3u

= 3 × 20

= 60 cm

(+ve as it is a real image)

Using lens formula

`1/v - 1/u = 1/f`

Where u= object distance, v= image distance and f = focal length of the lens

Putting all the values

`1/60 + 1/20 = 1/f`

`(1 + 3)/60 = 1/f`

`4/60 = 1/f`

`1/15 = 1/f`

f = 15 cm

Hence, the focal length of the lens is 15 cm.