What would be the size of image formed by concave mirror when the object is placed beyond the centre of curvature?

3. Find the size, nature and position of image formed when an object of size 1 cm is placed at a distance of 25 cm from a concave mirror of focal length 20 cm ?

Sol: Here we have been given the object distance and focal length, so first of all we will find out the image distance which will give us the position of image.

(i) Position of image

Here, Object distance, u	=	− 25 cm (To the left of mirror)
Image distance, v	=	? (To be calculated)
And, Focal length, f	=	− 20 cm (It is concave mirror)
Now, putting these values in the mirror formula :
1/f	=	1/v + 1/u
We get: 1/–20	=	1/v + 1/– 25
(or) – 1/20	=	1/v – 1/25
(or) 1/v	=	1/25 – 1/20
	=	4 – 5/100
	=	– 1/100
So Image distance, v	=	− 100cm

Thus, the position of image is 100 cm to the left side of mirror or 100 cm in front of mirror (Minus sign shows the left side of mirror).

(ii) Nature of image

Since the image is formed in front of the concave mirror, its nature will be “Real and Inverted”.

(iii) Size of image

To find the size of image, we will have to calculate the magnification first.

The magnification produced by a mirror is given by :
m	=	v/u
Here Image distance, v	=	− 100cm
Object distance, u	=	− 25cm
So, m	=	– (–100) / (– 25) = –4
Magnification,m	=	−4
We also have another formula for magnification, which is :
m	=	h2/h1
Here, Magnification,m	=	−4 (Found above)
Height of image,h2	=	? (To be calculated)
Height of object,h1	=	1cm (Given)
Now, putting these values in the above magnification formula, we get:
– 4	=	h2/1

Thus, the size of image is 4 cm long. The minus sign here shows that the image is formed below the principal axis.

That is, it is a real and inverted image.

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