Question

An object 4cm in size is placed at 25cm in front of concave mirror of focal length 15cm.At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and size of the image.

Answer 1

Given:

h₁ = 4 cm
u = -25 cm
f = - 15 cm

So, using mirror formula we have

    1/f = 1/v + 1/u
⇒ 1/-15 = 1/v + 1/-25
⇒-1/15 + 1/25 = 1/v
⇒-5+3/75 = 1/v
⇒-75/2 = v 
⇒ v= -37.5 cm

∴Screen should placed at distance of 37.5 cm from mirror to obtain a sharp      image.

Also, h₂/h₁ = -v/u
∴h₂ = -3/2 * 4
⇒ h₂ = -6 cm

∴ Image is real and inverted and size is 6 cm below principal axis.

Answer 2

ho=4cm. u= -25cm f= -15cm ( since it is concave mirror). v=? hi=?
1/v+1/u=1/f

1/v=1/f-1/u
1/v=1/-15 - 1/-25
1/v= -1/15 + 1/25
1/v= -2/75
v=-75/2
v=-37.5cm
hence, screen should be placed at a distance of -37.5cm
m=-v/u=hi/ho
75/2*(-25)=hi/4
hi= -6cm
size of image is -6cm
nature--- real and inverted(since v is -ve)