Question

List the new Cartesian sign convention for reflection of light by spherical mirror. Draw a diagram and apply these conventions for calculating the focal length and nature of spherical mirror which forms a 1/3 times magnified virtual image of an object placed 18 cm in front of it.

Answer 1

New Cartesian Sign Conventions for reflection of light by spherical mirrors are given below:

1. The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

2. All distances parallel to the principal axis are measured from the pole of the mirror.

3. All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along − x-axis) are taken as negative.

4. Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

5. Distances measured perpendicular to and below the principal axis (along −y-axis) are taken as negative.

`m=1/3`

u = -18 cm

f = ?

v = ?

`m=-v/u=1/3`

`=>v=-u/3=-((-18))/3=6` cm

Now, according to mirror formula

`1/v+1/u=1/f`

`1/6+1/((-18))=1/f`

`1/f=(3-1)/18`

`1/f=2/18`

`f = 9` cm

Since the focal length is positive so, it is a convex mirror.

Ray diagram: