Question

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

Answer 1

The following sign convention is used for measuring various distances in the ray diagrams of spherical mirrors:

• Object is always placed to the left of mirror
• All distances are measured from the pole of the mirror.
• Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative.
• Distances measured along y-axis above the principal axis are positive and that measured along y-axis below the principal axis are negative.

Since the image formed is magnified and virtual, the mirror is convex.

According to the convention

$u=-18cm$

$m=1/3=-\frac{v}{u}$

$⟹v=6cm$

From mirror equation,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$⟹f=\frac{uv}{u+v}$

$⟹f=9cm$