of Image by Calculation The focal length of a spherical mirror can be found using the formula 1 f 1
FOCAL LENGTH OF A SPHERICAL MIRROR2 f 1
f 1
u 1 v focal length, u object distance, image distance v Magnification
The height of the image is usually different from the height of the object.The magnifi- cation is the ratio of image height to object height.This ratio happens to be the same as the ratio of image distance to object distance.Therefore we get the formula
m v u
Sign convention In front of the mirror is considered to be positive.This means:
f 7 0 for a concave mirror, v 7 0 for a real image.
Concave mirrors When dealing with concave mirrors, write the formula as
You may use
1 f 1
u 1 v
use the previous formula (giving v its appropriate sign). Convex mirrors Use
the focus is always behind the mirror. 1
f 1 u 1 v SAMPLE PROBLEM 12A
An object, of height 4 cm, is placed 30 cm in front of a concave mirror of focal length 20 cm. (i) What is the distance of the image from the mirror? (ii) What is the nature of the image? (iii) What is the height of the image?
u f v
Fig 12.15: Ray diagram for a spherical mirror, showing the object distance and the image distance drawn accurately
2The distances in this formula ignore the curvature of the mirror and are taken to be the distance from the object to a line perpendicular to the principal axis, containing the pole of the mirror, as illustrated in Fig 12.15.
REFLECTION OF LIGHT 201
1 f 1
u 1 v . when dealing with a virtual image (writing v as a positive) or MAGNIFICATION
m m v
u v
u
magnification image distance object distance
MAGNIFICATION
m m v
u v
u
magnification image height object height
u 1 v
when dealing with convex mirrors as the image is always virtual and
