Q. A short linear object of length lies on the axis of a concave mirror of focal length at a distance from the pole. The length of the image will be.

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A

B

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D

Solution:

The concave mirror formula is
.... (i)
Since, for a given concave mirror, focal length is fixed, we partially differentiate Eq. (i) to get
or ...... (ii)
Multiplying Equation. (i) by , we get
or ..... (iii)
Using Equation. (iii) in Equation. (ii), we get

Given Therefore

The negative sign shown that image is longitudinally inverted. The magnitude of the size of the image is

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