Q-
A Concave mirror forms a real image of an
object kept at a distance of 9 cm from it.if
the object is taken away from the mirror
by 6 cm, the image size reduces to one-fourth of its
previous size find focal length of the mirror.
Answers
focal length of the mirror is -7 cm.
it is given that a concave mirror forms a real image of an object at a distance of 9cm from it. if the object is taken away from the mirror by 6cm, the image size reduces to one fourth of its previous size.
here object distance, u = -9cm
image distance = v
focal length = f
using formula, 1/v + 1/u = 1/f
⇒1/v + 1/-9 = 1/f ...........(1)
magnification, m = -v/-9 = I/O .......(2)
now new object distance, u' = -(9 + 6) = -15cm
size of image = 1/4 × initial size of image
⇒I' = I/4
so magnification, m' = -v'/-15 = (I/4)/O......(3)
using formula, 1/v' + 1/u' = 1/f
⇒1/v' + 1/-15 = 1/f ........... (4)
from equations (1) and (2),
-4v'/-15 = -v/-9
⇒4v'/5 = v/3
⇒12v' = 5v
from equation (4) we get,
12/5v + 1/-15 = 1/f.........(4)
from equations (1) and (4) we get,
12/5 × 1/-9 - 1/-15 = 12/5 × 1/f - 1/f
⇒-4/15 + 1/15 = 7/5f
⇒1/-5 = 7/5f
⇒f = -7 cm