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  • An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained?

Q 15.     An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and  the nature of the image.

 

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Object distance, u = -27 cm

Focal length, f = -18 cm

Let the image distance be v

As per the mirror formula

\\\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\ \frac{1}{-18}=\frac{1}{v}+\frac{1}{-27}\\ v=-54\ cm

The negative sign shows the image is formed in front of the mirror and is real.

Object size = 7 cm

\\Image\ size=magnification\times Object\ size\\ =-\frac{v}{u}\times O\\ =-\frac{-54}{-27}\times 7\\ =-14\ cm

A real, inverted and magnified image of size 14 cm is formed in front of the mirror.

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