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.