Chapter 23, Problem 27Q

To determine

To Compare:

The mirror equation and the lens equation, similarities and differences, especially the sign conventions for the quantities involved.

Answer to Problem 27Q

Solution:

The mirror equation and the lens equation are compared and analyzed as both the equations have the similar functional forms. According to sign conventions, f > 0 shows the converging lens or mirror and f < 0 shows the diverging lens or mirror. Similarly for both lens and the mirror, when d > 0, then it indicates the real image and when d > 0, it shows the virtual image.

Explanation of Solution

The mirror equation given by

$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

Where,

d_i is the image distance

d_o is the object distance

f is the focal length.

The same equation can be used for the lens also.

Both, equation describes the object and image distances to the focal length f.

The sign convention followed in the both equation have been analyzed:

The focal length is positive for converging lenses and negative for diverging lenses.

The focal length is positive for concave mirror and negative for convex mirror.

The image and the object distances (d_i and d_o)are positive if image or object is in front of the mirror. If either image or object is behind the mirror, the corresponding distance is negative.

The object distance d_o is positive if the object is on the side of the lens from which the light is coming. The image distance d_i is positive for the real image and negative for the virtual image.