The radius of curvature of a concave mirror is 24 cm and the image is magnified by 1.5 times. The object distance is???
The radius of curvature of a concave mirror is 24 cm and the image is magnified by 1.5 times. The object distance is???
It may be some mistake in the book.
In a spherical mirror, the focal length is half of radius of curvature. ie f = R/2
We have the mirror formula
1/v + 1/u = 1/f
We also have magnification formula
m = -v/u
here m = 1.5
So v = -1.5 u
in concave mirror magnified and virtual image is produced when we place the object inside focus. In this case image will be formed on the right side of mirror (v is positive). while focal length f and object distant u will be negative because they are on the left side of the mirror.
using v = -1.5 u and f = -12 in mirror formula
-1/1.5u + 1/u = -1/12
1/u - 2/3u = -1/12
1/3u = -1/12
u = -4 cm
The object is placed at a distance 4 cm on the left side of lens.
In a spherical mirror, the focal length is half of radius of curvature. ie f = R/2
We have the mirror formula
1/v + 1/u = 1/f
We also have magnification formula
m = -v/u
here m = 1.5
So v = -1.5 u
in concave mirror magnified and virtual image is produced when we place the object inside focus. In this case image will be formed on the right side of mirror (v is positive). while focal length f and object distant u will be negative because they are on the left side of the mirror.
using v = -1.5 u and f = -12 in mirror formula
-1/1.5u + 1/u = -1/12
1/u - 2/3u = -1/12
1/3u = -1/12
u = -4 cm
The object is placed at a distance 4 cm on the left side of lens.
