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

Step 1: Given data

The distance of the filament from the screen is 80 cm

The lens is converging which is a convex lens.

magnification(m) = 3

Step 2: Calculation of the focal length of the convex lens:

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 = $\frac{v}{u}$ = 3

Or,

$\Rightarrow$ 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 $\times$ 20

= 60 cm

(+ve as it is a real image)

Using lens formula; $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

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

Putting all the values

$\frac{1}{60}+\frac{1}{20}=\frac{1}{f}$

$\frac{1+3}{60}=\frac{1}{f}$

$\frac{4}{60}=\frac{1}{f}$

$\frac{1}{15}=\frac{1}{f}$

$f=15cm$

Hence

The focal length of the lens is 15 cm.