Question

A concave mirror produces image 10 mm of an object 2.5mm placed at 5 cm frm the mirror .calculate focal length of the mirror and the position of the image

Answer 1

Hi friend :)

Here is your answer -:

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10mm = 1 cm

$h_{1} = - 1cm \\ h_{2} = 2.5mm = 0.25cm \\ u = - 5cm \\ m = \frac{ h_{1}}{ h_{2}} = \frac{ - v}{u} \\ \frac{ - 1}{0.25} = \frac{ - v}{ - 5} \\ - 4 = \frac{v}{5} \\ v \: = - 20$
So, position of image = 20cm in front of mirror

now, using mirror formula , we get

1/f = 1/v + 1/u

1/f = 1/-20 + ( 1/ -5)

1/f = -1/20 + (-1/5)

1/f = -1 + (-4) / 20

1/f = -5/20 = -1/4

f = -4

focal length = -4 cm

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Hope it helps :)