Question : The rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its ends closer to the pole is 20 cm away from the mirror. The length of the image is
(a) 2 cm
(b) 4 cm
(c) 5 cm
(d) 6 cm
Doubt by Tannu
Solution :
In concave mirror
Focal length (f) = -10 cm
Let the position of end of the rod near the pole be u1
u1=-20 cm
f=-10 cm
v1=?
Using the Mirror Formula
1/v+1/u=1/f
1/v1+1/u1=1/f
1/v1=1/f-1/u1
1/v1=1/(-10)-1/(-20)
1/v1=-1/10+1/20
1/v1=-2/20+1/20
1/v1=-1/20
1/v1=-2/20+1/20
1/v1=-1/20
v1=-20 cm
|v1| = 20 cm
Let the position of the other end of the rod near away from the pole be u2
u2=-(20+10)=-30 cm
f=-10 cm
v2=?
Again Using Mirror Formula
1/v2+1/u2=1/f2
1/v2=1/f2-1/u2
1/v2=1/(-10)-1/(-30)
1/v2=-1/10+1/30
1/v2=-3/30+1/30
1/v2=-2/30
1/v2=-1/15
v2=-15 cm
|v2| = 15 cm
Hence, the length of the image will be
=|v1|-|v2|
=20-15
= 5 cm
Hence, (c) 5 cm, would be the correct option.
