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in Optics by (63.5k points)

A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

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u = – 27 cm, R = – 36 cm,

f = -R/2 = -36/2 = - 18cm.

Height of object, h = 2.5 cm, v = ?

1/v + 1/u = 1/f

As,

1/v = 1/f - 1/u = 1/-18 - 1/(-27) = -1/18 + 1/27 = (-3 + 2)/54 = -1/54 = - 54cm

The screen should be placed at 54 cm from the mirror on the same side as the object.

m = h'/h = - v/u

magnification,

or, h' = - v/u x h = -((-54)/(-27)) x 2.5 = - 2 x 2.5 = - 5cm.

The image is real and inverted. If the candle is moved closer to the mirror, the screen has to be moved away from the mirror.

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