Question

justify your reasoning giving two reasons In each case .
A 2cm high object is placed at a distance of 32 cm from a concave mirror. The image is real real inverted and 3 cm in size. Find the focal length of the mirror and the position where the image is formed. ​

Answer 1

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❇A 2cm high object is placed at a distance of 32 cm from a concave mirror. The image is real real inverted and 3 cm in size. Find the focal length of the mirror and the position where the image is formed.

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Given:-

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h=2cm

dist=32cm

size=3cm

To Find:-

Focal Length &position of image.

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Concave mirror:-

u = -32 cm , h = 2 cm , h' = -3 cm

m = h'/h = -3/2

m = -v/u = -3/2

=> v = 3 u /2 = - 48 cm

1/f = 1/ u + 1/v

= -1/48 - 1/32

= - 5/96

f = - 19.2 cm

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The focal length of the mirror=-19.2cm

The position where the image is formed.

=-48cm

Answer 2

Answer:

Given:

Height of object = 2 cm

Object distance = - 32 cm

Image height = 3 cm

Image is real and inverted.

To find:

Focal length of mirror and image distance.

Calculation:

$\frac{hi}{ho} = - ( \frac{v}{u} )$

$= > \frac{ - 3}{2} = - ( \frac{v}{ - 32} )$

$= > v = - 48cm$

Now, applying Mirror Formula :

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

$= > \frac{1}{f} = ( \frac{1}{ - 48}) + ( \frac{1}{ - 32} )$

$= > \frac{1}{f} = ( \frac{ - 5}{96})$

$= > f = - \frac{96}{5} cm$

$= > f = -19.2 \: cm$

So final answer is focal length is -19.2 cm.