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

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., $\frac{1}{v}$ - $\frac{1}{u}$ = $\frac{1}{f}$
So, $\frac{1}{60}$+$\frac{1}{20}$ = $\frac{1}{f}$
Therefore, f = 15 cm