An object 4 cm in size is placed at 25cm

The questions is

An object 4 cm in size is placed at a distance of 25 cm from a concave mirror of focal length 15 cm. At what distance from the mirror should the screen be kept so that a sharp image of the object can be obtained on screen? Find the nature and height of the image.

Solution Explaination:

Given that f = -15 cm; u = -25 cm ; ho= 4 cm; v = ?
The mirror formula is 1/f = 1/u + 1/v = 1/-15 = 1/-25 + 1/v
1/v = 1/25 - 1/15
1/v = (3-5)/ 75 =-2/ 75
v =-37.5 cm
The screen should be placed 37.5 cm from the pole of mirror and the image is real.
Magnification, m = -v/u =hi/ho= hi / 4 = 37.5 / 25
hi = (37.5 / 25 )x 4 = -6 cm
So the image is enlarged and inverted.


b) Converging mirror is actually concave mirror!

hi = -4cm(real and inverted.)
ho = 1cm
u=-20cm
(a) v=?

hi/ho=-v/u

where,
hi=height of the image
ho=height of the object
v=distance of the image from the mirror
u=distance of the object from the mirror

-4/1=-v/-20
4 = v/20
v = -80cm

Let focal length of the mirror to be 'f'

1/f = 1/v + 1/u

1/f = 1/-80 + 1/(-20)
1/f = 1/-80 - 1/ 20
1/f = -5/80
f = -80/5cm = -16 cm

what is concave mirror?

Concave mirrors are mirrors that have been curved inwardly at the edges. These mirrors are often used in phototherapy (light therapy) to treat depression and anxiety disorders.

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