What is the magnification produced by a concave lens of focal length 1

What is the magnification produced by a concave lens of focal length 10 cm, when an image is formed at a distance of 5 cm from the lens?

2.0
1.0
0.5
0.33
This question was previously asked in
UPSC NDA-1 – 2022
The correct option is C.
For a lens, the lens formula is $1/f = 1/v – 1/u$ and magnification is $m = v/u$. For a concave lens, the focal length $f$ is negative, and it forms virtual, upright, and diminished images, typically on the same side as the object (so image distance $v$ is negative).
Given focal length $f = -10$ cm (concave lens). The image is formed at a distance of 5 cm from the lens. Since it’s a concave lens, the image is virtual and formed on the same side as the object, so image distance $v = -5$ cm.
Using the lens formula: $1/f = 1/v – 1/u$
$1/(-10) = 1/(-5) – 1/u$
$-1/10 = -1/5 – 1/u$
$1/u = -1/5 + 1/10$
$1/u = -2/10 + 1/10$
$1/u = -1/10$
$u = -10$ cm (object distance is 10 cm in front of the lens).
Magnification $m = v/u = (-5 \text{ cm}) / (-10 \text{ cm}) = 0.5$.
The magnification is 0.5, indicating a diminished image.
Exit mobile version