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Question
An object of height 2 cm is placed at a distance of 20 cm in front of a concave mirror of a focal length of 12 cm. Find the position, size, and nature of the image.
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Solution 1
The image is 30 cm in front of the mirror, 3 cm high, real, inverted and magnified.
Solution 2
Object distance (u) = -20 cm
Focal length (f) = -12 cm
Image size (I) = 2 cm
Let the image distance be 'v' then
`1/u + 1/v = 1/f`
Or, `1/(-20) + 1/v = 1/(-12)`
Or, `1/v = -1/12 + 1/20 = (-5 + 3)/60`
Or, `1/v = -2/60`
Or, v = -30 cm
Now, `"Image size (I)"/"Object size (O)" = -"Image distnace (v)"/"Object distnace (u)"`
Or, `I/2 = -((-30)/-20)`
Or, I = -3 cm
∴ The image is 30 cm in front of the mirror.
The image is 3 cm high with the following characteristics:
- Real
- Inverted
- Magnified
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