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The radius of curvature of a concave mirror is 50 cm. Where should an object be placed in the mirror, so as to form its image at infinity? Justify your answer.

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Best answer

Given;

Radius of Curvature(R) = 50cm;

R = 2f 

⇒ 50 = 2f 

⇒ f = \(\frac{50}2\) = 25 cm

Focal length = 25cm.

When an object is kept at the focus of the concave mirror then the image is formed at infinity. 

This can be shown as below: 

The Mirror formula is given by: 

\(\frac{1}{F}\,=\,\frac{1}{v}\,+\frac{1}{u}\)

Where, F is the focal length of the mirror 

v is the image distance from the pole of the mirror 

u is the object distance from the pole of the mirror 

On solving for v, we get 

\(\frac{1}{v}\,=\,\frac{1}{f}\,-\frac{1}{u}\)

If F=u=25 cm, we get 

\(\frac1v\) = 0 or v = \(\frac10\) = ∞

Therefore the object should be placed at 25cm from the pole of the concave mirror to get an image at infinity.

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