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Question

An object is placed at a distance of 6 cm from a convex mirror of focal length 12 cm. Find the position and nature of the image.

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Solution

Object distance[u] = -6cm [New Cartesian Sign Convention]

Focal length[f] = 12cm

Image distance[v] = ?

1 over v plus 1 over u equals 1 over f [Mirror Formula]

1 over v equals 1 over f minus 1 over u

1 over v equals 1 over 12 minus fraction numerator 1 over denominator negative 6 end fraction

1 over v equals 1 over 12 plus 1 over 6

1 over v equals 3 over 12

v = 12 over 3 = 4cm

The image is 4 cm behind the mirror.

Magnification [m] = straight h to the power of apostrophe over straight h equals fraction numerator negative straight v over denominator straight u end fraction

m = fraction numerator negative 4 over denominator negative 6 end fraction

m = 0.66

The image is virtual,erect and diminished.


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