# A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what

76 views
in Physics
closed
A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

by (71.8k points)
selected by

Here, object size, h_(1) = 4.5 cm
object distance, u = -12 cm
focal length, f = +15 cm
image distance, v = ? (to be calculated)
magnification,m = ?
As 1/u + 1/v = 1/f , 1/v = 1/f -1/u
Putting u = -12 cm and f = + 15 cm , we get
 1/v = 1/15 - 1/(-12) = (4+5)/60 or v = 60/9 = 6.7 cm
i.e., image is formed 6.7 cm behind the convex mirror. It must be virtual and erect.
If h_(2) is size of the image, then m = h_(2)/h_(1) = (-v)/u or m = h_(2)/h_(1) =(-(6.7))/(-12) = 0.558
i.e., h_(2) = 0.558 h_(1) = 0.558 xx 4.5 = 2.5 cm
As the needle is moved farther from the mirror, image moves away from the the mirror till it is at focus F of the mirror. The size of the image goes on decreasing.