Question

An Object is held at 30 min front of a convex mirror
of focal length 15 cm. At what distance from the convex mirror be held so that images in the two images coincide with each other?

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Answer 1

f = -15 cm u = -30 cm and the image distance will be calculated using 1/f = 1/v + 1/u or 1/v = 1/f + 1/u = 1/-15 - 1/30 or 1/v = (-2 - 1)/30 = -3/30 thus, we have v = -10 cm now, the image formed would be 30cm behind the convex so the total distance between the object and image will be = 30cm + 10cm = 40cm. The plane mirror needs to placed at a distance of 20cm from the object in order for the image to coincide as it will form 20 cm behind it. The total distance would thus have to be 40cm.