Question

Mirror equation for convex mirror and concave mirror are
A. Same
B. Different
C. Different depending on the object position.
D. Same for only a few image positions.

Answer 1

Hint-The mirror equation is the equation that gives the relationship between object distance, image distance and focal length of mirror. By analyzing the mirror equation for concave and convex mirror we can find the correct answer to this question.

Step by step solution:
Mirror equation is an equation connecting the object distance, image distance and the focal length of a mirror.
While deriving the formula for concave and convex mirror certain sign conventions are used. They are
(1) all the distances must be measured from the pole of the mirror.
(2) The distance of a real image is taken as positive whereas the distance of a virtual image is taken as negative.
(3) Focal length of the concave mirror is taken as positive and focal length of the convex mirror is taken as negative.
The mirror equation derived using these sign conventions is the same for concave and convex mirrors.
The mirror equation common to both concave mirror and convex mirror is given as
$\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$
Where f is the focal length, v is the image distance, u is the object distance.

Since the mirror equation for convex mirror and concave mirror is the same, the correct answer is option A.

Note:Remember that the mirror equation is the same for convex and concave mirrors. While doing problems using mirror formula, we should take care of the sign convention before substituting the values. The focal length is positive for concave mirror and negative for convex mirror. Object distance in front of the mirror is positive and behind a mirror is negative. Image distance is positive for real image and negative for virtual image.