Question

Determine the image distance in each of the following.
a) A converging mirror has a focal length of 15 cm. An object is placed (i) 40 cm, and (ii) 10 cm
from the mirror.
b) A diverging mirror has a focal length of -20 cm. An object is placed (i) 10 cm, and (ii) 30 cm
from the mirror.

Show Steps.

Answer 1

Hey there

Lemme know you first what is conversing and diverging mirrors are

• Converging mirror :-

→ also known as the Concave mirror

→it has the reflecting surface inside of the mirror

→ Focal length can be +Ve ,or -ve

•Diverging mirror :-

→ Also know as Convex mirror

→ it has the reflecting surface inside of the mirror

→ Focal length is always +Ve

Now coming to our Questions

[ A ] For converging mirror :-

Given -

Focal length , f = - 15 cm

when object is placed in [ ¡ ] = - 40 cm

Image distance = ?

Using mirror formula

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = > \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{ - 15} - \frac{1}{ - 40} = \frac{ - 1}{15} + \frac{1}{40} = \frac{ - 8+ 3}{120} = \frac{ - 5}{120} = > v = \frac{ - 120}{5} = -24 \: cm$

When [ ii ] u = - 10 cm

$\frac{1}{v} = \frac{ - 1}{15} + \frac{1}{10} = > \frac{1}{v} = \frac{ - 2 + 3}{30} = v = + 30 \: cm$

Now coming to the Next question

[ B ] For Diverging mirror

focal length , f = 20 cm
object is placed , in [ 1 ] 10 cm

$\frac{1}{v} = \frac{1}{20} - \frac{1}{ - 10} = > \frac{3}{20} = 6.67 \: cm \:$

when u = 30 cm

$\frac{1}{v} = \frac{1}{20} + \frac{1}{30} = > \frac{3 + 2}{60} = \frac{5}{60} = v = + 12 cm$

Hope this helps ya ☺

Answer 2

  {A} according to the mirror formula
1/v+1/u=1/f where 'f' is the focal length 'u' is the object distance from mirror and 'v' is the image distance
therefore, for (i)
1/v+1/-40=1/-15-40+v/-40v=1/-15(-40+v)*(-15)=-40v
600-15v=-40v600=-40v+15v600=-25v600/25=-v24=-v
v=-24the image formed in converging mirror is behind the mirror so it is given the negative sign  same process for (ii)
{b}in an diverging mirror the focal length is negative therefore according to the mirror formula for (ii)
1/v+1/u=1/f1/v+1/30=1/-2030+v/30v=1/-20-20*(30+v)=30v-600-20v=30v-600=30v+20v-600=50v-600/50=vv=-12 hence in diverging mirror image distance is 12cmsame process for (i)