Question

An object 4 cm height is placed at 15 cm in front of a concave lens of focal length 10 cm. at  what distance from the mirror should a screen be placed to obtain a sharp image of the object.  Calculate the height of the image.​

Answer 1

Given :-

f = - 10 cm

u = - 15 cm

h₂ = 4 cm

Solution :-

Using the mirror formula,

1/f = 1/v + 1/u

⇒ 1/v + 1/-15 = 1/- 10

⇒ 1/v = 1/- 10 + 1/15

⇒ 1/v = (- 15 + 10)/150

⇒ 1/v = - 5/150

⇒ v = - 30 cm

Thus, to obtain a sharp image of the object the screen should be placed in front of the mirror at a distance of 30 cm from the mirror.

Magnification, m = - v/u = h₁/h₂

⇒ m = - 30/- 15

⇒ m = - 2

⇒ h₁ = - 8 cm

Hence, the image height will be 8 cm.

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