Question

An object is placed at 15cm in front of a concave mirror of radius of curvature

20cm. Find the position and magnification of the image.​

Answer 1

Answer:

u= -15

R=15 so,

f= -15/2

by mirror formula,

1/f=1/v+1/u

so, v=15cm

m= -v/u

m= -1

Answer 2

Answer:

The position and magnification of the image are -30 cm and -2 respectively.

Explanation:

We will use the mirror formula to solve this question. Which is given as,

$\frac{1}{f} =\frac{1}{v}+\frac{1}{u}$       (1)

Where,

f=focal length of the mirror

v=image distance from the mirror

u=object distance from the mirror

From the question we have,

u=-15cm

The radius of curvature of concave mirror(R)=-20cm

The focal length of the mirror is given as,

$f=\frac{R}{2}$        

So,

$f=\frac{-20}{2}=-10cm$     (2)

By substituting the required values in equation (1) we get;

$\frac{1}{-10} =\frac{1}{v}+\frac{1}{-15}$

$\frac{1}{v}=\frac{1}{-10}+\frac{1}{15}$

$\frac{1}{v}=\frac{-3+2}{30}$

$\frac{1}{v} =\frac{-1}{30}$

$v=-30cm$       (3)

And the magnification of the mirror is given as,

$m=\frac{-v}{u}$     (4)

By substituting the required values in equation (4) we get;

$m=\frac{-(-30)}{-15}$

$m=-2$

Hence, the position and magnification of the image are -30 cm and -2 respectively.