CBSE Class 12-science Answered
(i)
For a concave mirror, focal length (f) is negative, f<0
When an object s placed on the left side of the mirror, the object distance (u) is negative, u<0
Using lens formula
1/ v - 1/ u = 1/f
1/v = 1/f -1/u ......(i)
The object lies between f and 2f
2f<u<f
1/2f>1/u>1/f
1/f -1/2f<1/f-1/u<0 .......(ii)
Using equation (i) we get
1/2f< 1/v<0 if, 1/v is negative
or, 1/2f<1/v
or, 2f>v
-v>-2f
Therefore, the image lies beyond 2f
(ii)
For a convex mirror, the focal length (f)>0 and u<0
1/v +1/u = 1/f
1/v = 1/f -1/u
Using equation (ii) we get
1/v<0
v>0
Hence a convex mirror is always produces a virtual image.
(iii)
For a convex mirror, the focal length (f)>0 or positive and u<0
Using les formula
1/v +1/u = 1/f
1/v = 1/f -1/u
Since u<0
Then , 1/v>1/f
v>f
(iv)
For a concave mirror, f is negative, i.e, f<0 and u<0
It is placed between f and pole
Therefore,
f>u>0
1/f<1/u<0
1/f-1/u<0
For negative distance v, using lens formula
1/v +1/u =1/f
1/v = 1/f -1/u
1/v<0
v>0
The image is formed on the right side of the mirror.
Hence, it is virtual image
For u<0 and v<0
Then,
1/u>1/v
v>u