Question

A converging mirror forms a real image of height 4cm of an object of height 1cm placed 20 cm away from the mirror: Calculate the image distance. What is the focal length of the mirror?

Answer 1

h2 = - 4 cm (real iamge)

h1 = 1 cm

u = - 20 cm

(i) v = ?

m = h2/h1 = - (v/u)

⇒ -4/1 = -(v/-20)

⇒ v = -80 cm

Image forms in front of the concave mirror.

(ii) f = ?

1/v + 1/u = 1/f

1/-80 + 1/-20 = 1/f

1/f = - (1/80) – 1/20 = (-1 – 4)/80 = - (5/80)

f = - 16 cm

Answer 2

Given

---------

Mirror is concave .

h1=-4 cm

h2=+1cm

u=-20cm

Solution

________

we know that

m= h1/h2=-v/u

$\frac{ - 4}{1} = - \frac{v}{ - 20}$

=>-4=v/20

=> v= -80 cm

Now, by mirror formula

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

=>1/-80 + 1/-20 = 1/f

=>

$\frac{ - 1 - 4}{80} = \frac{1}{f}$

-5/80=1/f

=>-1/16=1/f

=>f=-16 cm

Hence,image distance is -80 cm and focal length is -16cm.