Question

List the sign conventions for reflection of light by spherical mirrors. Draw a
diagram and apply these conventions in the determination of focal length of a spherical mirror which forms a three times magnified real image of object placed 16 cm in front of it.

Answer 1

Sign conventions for reflection of light by spherical mirror are:

1. The object is always placed to the left of the mirror.
2. All the distances parallel to the principal axis are always measured from the pole of the spherical mirror.
3. All the distances’ measured along the direction of incident light (along + ve X-axis) are considered to be positive.
4. Those distances measured opposite to the direction of incident light (i.e along – ve X-axis) are taken as negative.
5. The distances measured in upward direction, i.e. perpendicular to and above the principal axis (along + ve y-axis) are taken as positive.
6. The distances measured in the downward direction, (along – ve y axis), i.e. perpendicular to and below the principal axis are take as negative.

From the question

u = – 16 cm,

m = – 3 for real image

But m = \(\frac{−v}{u}\) = -3

υ = 3u = – 3(- 16)

= – 48 cm

Using mirror formula

\(\frac{1}{f}\) = \(\frac{1}{v}\) + \(\frac{1}{u}\)

We get \(\frac{1}{f}\) = \(\frac{1}{−48}+\frac{1}{−16}\)

= \(\frac{−1−3}{48}\)

= \(\frac{-4}{48}\) = \(\frac{-1}{12}\)

f = – 12 cm