An object is placed at a distance of 24cm in front of a convex mirror. Its image is formed at a distance at 12 cm behind the mirror. The focal length of the mirror is:

Correct option is A

Sol: The correct answer is (a) 24cm

Given:

The object distance u is -24 cm (negative because it's in front of the mirror),

The image distance v is 12 cm (positive because it's behind the mirror).

Formula used:

​$$\frac1=\frac1+\frac1$$

f is the focal length,

v is the image distance,

u is the object distance.

Solution:

​$$\frac1=\frac1{12}+\frac1{−24}$$

​​calculate each term:

​$$\frac1{12}$$ = 0.0833

​$$\frac1{−24}$$ = - 0.0417

​Add these values:

​$$\frac1$$ = 0.0833−0.0417 = 0.0416

​take the reciprocal to find the focal length:

f = $$\frac1{0.0416}$$ = 24.04 cm

​So, the focal length of the convex mirror is approximately 24 cm.​

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