Question

A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror. Find the position of the image and the focal length of the mirror.

Answer 1

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A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror.

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asked Aug 1, 2019 in Class X Science by priya12 (-12,638 points)

A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror. Find the position of the image and the focal length of the mirror.

reflection of light

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answered Aug 1, 2019 by aditya23 (-2,160 points)

h2 = 1cm = 10mm (real image), h1 = 2.5mm, u = -5cm = -50mm

m = - h2/h1

m = - (10/2.5)

m = -4

and we know that

m = - (v/u)

and we know that

m = - (v/u)

-4 = - (v/(-50)

V = - 200 mm

V = - 20 cm

The image is formed 20 cm in front of the mirror.

And,

1/v + 1/u = 1/f

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

1/f = -25/100

f = - 4 cm

Answer 2

The position of the image remains 20cm from the mirror. The focal length of the mirror is -4cm.

Explanation:

h1 = -1cm = 10mm

h2 = 2.5mm = 0.25cm

u = -5cm = -50mm

$m = \frac{h1}{h2} = \frac{-v}{u}$

 $\frac{-1}{0.25} = \frac{-v}{-5}$

$-4 = \frac{v}{5}$

v =-20 (position of the image)

And,  $\frac{1}{v} +\frac{1}{u} =\frac{1}{f}$

$\frac{1}{-20} + \frac{1}{-5} = \frac{1}{f}$

$\frac{1}{f} = -\frac{-25}{100}$

f = - 4 cm

Focus of the mirror is -4cm.

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