Question

the filament of a lamp is 80cm 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. 1/v - 1/u = 1/f
So, 1/60+1/20 = 1/f
Therefore, f = 15 cm