Question

An object is placed at a distance of $40\, cm$ in front of a concave mirror of focal length $20\, cm$. The nature of image is

• A. real and inverted and of smaller size
• B. virtual and erect and of same size
• C. real and erect
• D. virtual and inverted

Answer 1

Answer: (A)

Distance of object u = - 40 cm.
Focal length of concave mirror f = - 20 cm.
By mirror formula
$ \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
or $ \frac{1}{v}=\frac{1}{f}-\frac{1}{u}$
$\therefore \frac{1}{v}=\frac{1}{-20}-\frac{1}{(-40)}$
$ = \frac{1}{-20}+\frac{1}{40}$
or $ v = - 40\, cm$
Negative sign implies that image is in front of concave mirror,
hence image is real.
Magnification produced by concave mirror
$ m = - \frac{v}{u}=-\frac{(-40)}{(-40)}=-1$
The image is of the same size and inverted.