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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
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.
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