A mirror forms an image with magnification 1/4. The distance between the object and image is 40 cm. The focal length of the mirror is:
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Question

A mirror forms an image with magnification 1/4. The distance between the object and image is 40 cm. The focal length of the mirror is:

G1 Physics · Accepted Answer

The positive magnification indicates an erect virtual image. Using magnitudes, let image distance be v and object distance be u. For a mirror, |m| = v/u = 1/4, so u = 4v. For a virtual image behind the mirror and object in front, their separation is u+v = 40 cm. Thus, 4v+v = 40 ⇒ v = 8 cm, u = 32 cm. Using the signed mirror relation with u = -32 cm and v = +8 cm: 1/f = 1/v + 1/u = 1/8 - 1/32 = 3/32. Hence, f = 32/3 cm ≈ 10.7 cm. Correct option: C.