Question

The relation between $ u,v $ and $ f $ for a mirror given by
(A) $ f = \dfrac{{u \times v}}{{u - v}} $
(B) $ f = \dfrac{{2u \times v}}{{u - v}} $
(C) $ f = \dfrac{{u \times v}}{{u + v}} $
(D) $ f = \dfrac{{u - v}}{{u + v}} $

Answer 1

Hint: Here $ f $ is the focal length,which is positive for a concave mirror, and negative for a convex mirror. When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted. Positive means an upright image.

Complete step by step answer:
Mirror formula,
The equation connecting the distance between mirror and object, distance between mirror and image and the focal length of the mirror is called mirror formula.
 $ \dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v} $
By cross multiplication we get the focal length of concave mirror,
 $ f = \dfrac{{uv}}{{u + v}} $
The relation between $ u,v $ and $ f $ for a mirror is given by
 $ f = \dfrac{{u \times v}}{{u - v}} $
Therefore, the correct option is (C) $ f = \dfrac{{u \times v}}{{u + v}} $
Magnification is the increase in the image size produced by a spherical mirror with respect to the object size. It is the ratio of height of the image to the height of the object and is denoted as m.

So, the correct answer is “Option C”.

Note:
Image formation by a concave Mirror for a real object close to the mirror but outside of the center of curvature, the real image is formed between $ C $ and $ f $ , no image is formed. The reflected rays are parallel and never converge. Convex mirror always forms virtual images because the focal point and the center of curvature of the convex mirror are imaginary points that cannot be reached. So they are projected on a screen.