Question

An object is kept in front of a concave mirror of focal length 20cm. The image is three times the
size of the object. Calculate two possible distance of the object from the mirror.​

Answer 1

Explanation:

The image is three times the size of the object. So there are two cases.

Case 1. For real image

m=−

u

v

=−3

v=3u

Using mirror’s formula

f

1

=

v

1

+

u

1

−20

1

=

3u

1

+

u

1

u=

3

−80

cm

Case 2. For virtual image

m=

u

−v

=+3

v=−3u

Again using mirror’s formula

−20

1

=

−3u

1

+

u

1

u=

3

−40

cm

The possible values of u are

3

−80

cmand

3

−40

cm.

Answer 2

Answer:

$\purple{ \boxed{\texttt{Answer}}}$

Answer :-

(a) 80/3 cm

(b) -40/3 cm

Solution :-

Given that, image size is 3 times object size. Thus magnification is ±3.

(a) For M = +3,

v/u = +3

v = 3u

Using mirror formula,

1/f = 1/v + 1/u

1/20 = 1/3u + 1/u

Solving this,

u = 80/3 cm

(b) For M = -3,

v/u = -3

v = -3u

Using mirror formula,

1/f = 1/v + 1/u

1/20 = 1/-3u + 1/u

Solving this,

u = -40/3 cm