Question

Find the size, nature and position of image formed by a concave mirror, when an object of size 1cm is place at a distance of 15cm. Given focal length of mirror is 10cm.

Answer 1

Hey!!
The given mirror is a concave mirror thus sign convention it's focal length will be negative.

This here
f = -10 cm
u = -15cm
h(height of object) = 1cm

we have to find
size , nature , position of image formed .

Thus using mirror equation :-
1/f = 1/u+1/v
=>1/v = 1/f-1/u
=> 1/v = -1/10+1/15
=> 1/v = -1/30
=> v = -30 { thus image will be formed beyond center
Now magnification
m = -(v/u) = h'/h
m = -(-30/-15)
=> m = -2
HENCE the image formed will be real and inverted and magnified.

Now m = h'/h
2 = h'/1
=> h' = 2cm
hence the size of the image will be doubled

Answer 2

Obj size =1 cm

Obj. distance =-15cm

Focal length=-10cm

V=?

1/v+1/u=1/f

1/v+1/-15=1/-10

1/v-1/15=1/-10

1/v=1/-10+1/15

1/v=-3+2/30

1/v=-1/30

Now we will do reciprocal of 1/v that is v and 1/-30 is -30 .

Value of v is -30

Mag.=image size /object size = -v/u

=image size/1 = -(-30)/-15

=image size = -2

Location of image is between pole and focus.

Nature of image is real and inverted.

Hope this helps you a lot!!!!!!!!!