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  4. A concave mirror gives an image three times as large as its object placed at a distance of 20 cm from it. For the image to be real, the focal length should be

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Q. A concave mirror gives an image three times as large as its object placed at a distance of $20\, cm$ from it. For the image to be real, the focal length should be

COMEDKCOMEDK 2015Ray Optics and Optical Instruments

Solution:

Here, for real image, $m = - 3$ or $- \frac{v}{u} = - 3$
$\therefore \:\:\:\:\: v = 3 u$
Also, $u = - 20 \, cm , $ so $v = - 60 \, cm , f = ?$
Using mirror formuIa, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f} $
$\frac{1}{-60} + \frac{1}{-20} = \frac{I}{f}$
$ - \frac{4}{60} = \frac{1}{f} ; \:\: \therefore \:\: f = 15 \, cm$