An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Focal length of concave lens (OF1), f = −15 cm
Image distance, v = −10 cm
According to the lens formula,
1/v – 1/u = 1/f
1/u = 1/v – 1/f = -1/10 – 1/(-15) = -1/10 + 1/15 = -5/150
U = -30 cm
The negative value of u indicates that the object is placed 30 cm in front of the lens.

Focal length of convex mirror, f = +15 cm
Object distance, u = −10 cm
According to the mirror formula,
1/v – 1/u = 1/f
1/v = 1/f – 1/u = 1/15 + 1/10 = 25/150
V = 6 cm
The positive value of v indicates that the image is formed behind the mirror.
Magnification, m = – Image Distance / Object Distance = – v/u = -6/-10 = +0.6
The positive value of magnification indicates that the image formed is virtual and erect.

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