Question

A candle flame 3 cm high is placed at a distance of
3 m from a wall. How far from the wall must a concave mirror be placed so that it may form 9 cm
high image of the flame on the same wall ? Also
find the focal length of the mirror.
(Ans. 4.5 m, - 1.125 m)​

Answer 1

Given:

The height of flame object is Hi=9 cm

The height of flame image is Ho= 3 cm

The distance is Z= 3 m

To find:

The focal length of the mirror and the distance from the wall.

Solution:

The ratio of flame height is

Hi/Ho=9/3

=3 cm

The ratio of distance be

Di/Do= 3

Di=3.Do

As Z=Di

Therefore

Z=3Do

Therefore the

Di=4.5

Do=1.5

Now the using the lens formula

1/f=1/v+1/u

1/f=1/1.5+1/4.5

1/f=4/4.5

f=1.125 m

So the focal length is 1.125 and distance is 4.5 m

Answer 2

Answer:

u=4.5 m

Explanation:

v=u+3

m=hi/ho

m=-9/3

m=-3

for real image -v/u

(u+3)/u=3

3u=u+3

2u=3

u=3/2=1.5

(u+3)m

u=1.5*3

u=4.5m

or 450 cm