A rod of length 10cm lies along the principle axis of a concave mirror of focal length 10cm in such a way that its end closer to the pole is 20cm away from the mirror. What is the length of the image
Given:
Length of the rod, l = 10cm
Focal length of the concave mirror, f = -10cm (negative sign because it is a concave mirror)
Distance of rod from mirror, u = -20cm (negative sign because it is measured in the direction opposite to the incident light)
Using the mirror formula:
1/f = 1/v + 1/u
Substitute the given values:
1/-10 = 1/v + 1/-20
Solving for v:
-1/10 = 1/v - 1/20
-1/10 = (2 - v)/2v
-2v = -10
v = 5cm
The image is formed at a distance of 5cm from the mirror. To find the length of the image, we use the magnification formula:
Magnification, M = -v/u
Substitute the values of v and u:
M = -5/-20
M = 1/4
The magnification is 1/4. This means that the image is one-fourth the size of the object.
Length of the image, l' = M*l
Substitute the values of M and l:
l' = (1/4)*10
l' = 2.5cm
Therefore, the length of the image formed by the concave mirror is 2.5cm.