For a concave mirror of focal length 20cm

Asked by admin @ 25/08/2021 in Physics viewed by 292 People

A concave mirror of focal length 20cm produces an image twice the height of an object .if the image is real ,then the distance of the object from the mirror is?

Answered by admin @ 25/08/2021

Hello Dear.

Here is the answer---

Given ⇒

Focal Length of the Mirror = 20 cm. (negative)

Let the Height of the Object be H.
∴ Height of the Image = 2H

Now,
Magnification = H₁/H₀
= 2H/H
= 2

Also, m = -v/u
2 = -v/u
⇒ v = -2u

Now,
Image Distance = -2u
Object distance = u

Using the Mirror Formula,

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
⇒ $\frac{1}{-20} = \frac{1}{-(-2u)} + \frac{1}{u}$
⇒ $\frac{1}{-20} = \frac{1 + 2}{2u}$
⇒ 2u = -20 × 3
⇒ 2u = -60
⇒ u = -30 cm.

∴ Distance of the Object from the mirror is 30 cm. Negative size shows that the object is kept on the side of the mirror.

Hope it helps.

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For a concave mirror of focal length 20cm

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