Question

(a) For concave mirror, focal length is taken as …………….
(b) For convex mirrors, the radius of curvature is taken as ………………..
(a). a = positive, b = negative
(b). a = negative, b = positive
(c). a = positive, b = positive
(d). a = negative, b = negative

Answer 1

Hint: To solve this type of question we must know the difference between concave and convex mirrors. Now, the focal length of concave mirror and convex mirror is given by the formula ${\displaystyle \frac{1}{u}}+{\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{f}}$ and relation between focal length and radius of curvature can be given as $f={\displaystyle \frac{R}{2}}$. Using this formula, the question can be solved easily.

Complete step-by-step answer:

Now in question we are asked to find whether the focal length of the concave mirror is positive or negative.
Before, determining whether the focal length is positive or negative we will understand what is focal length. The distance between the pole P of the concave mirror and the focus F is the focal length of the concave mirror.
Now, we know that the image formed by a concave mirror is always a real and inverted image and it is in front of the mirror.
Now, we know that the formula of focal length of concave mirror is given by ${\displaystyle \frac{1}{u}}+{\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{f}}$.
Where, u is the distance of object from the mirror, v is the distance of image formed from the mirror and f is the focal length of the mirror.
Now, from the formula it can be observed that the value of focal length depends on image distance and position of image.

And in concave mirror v both are in front of the mirror as shown in figure above, so, image distance is positive. Thus, the focal length of the concave mirror is always taken as positive.
Now, considering the convex mirror, we know that formula of concave mirror and convex mirror is same i.e. ${\displaystyle \frac{1}{u}}+{\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{f}}$.

Now, from the figure it can be observed that the image formed by the convex mirror is virtual, upright and behind the mirror as image distance is negative. Thus, the focal length of the convex mirror is negative.
Now we know the relation between focal length and radius of curvature i.e. $f={\displaystyle \frac{R}{2}}$. So, from this expression it can be said that focal length is directly proportional to radius of curvature. Thus, the radius of curvature of the convex mirror will also be negative.
Hence, option (a) is correct.

Note: For solving such type of questions students must know the sign convention system of concave mirror i.e. if the image is in front of the mirror and on the same side of the object distance then it is positive image distance and if it is formed behind the mirror then it is negative image distance. Students must also know the relation between image distance (v), object distance (u), focal length (f) and radius of curvature (R) for all the mirrors. By this the problem can be solved very easily.