A concave mirror of radius of curvature 50 cm is used to form an image of an object kept at a distance of 25 cm from the mirror on its principal axis. What will be the position of the image from the mirror?

The correct answer is At infinity.

Key Points

To find the position of the image formed by a concave mirror, you can use the mirror formula:

• \({1\over f} = {1\over u}+{1\over v}\)
• where:
  • f is the focal length of the mirror,
  • u is the object distance (distance of the object from the mirror),
  • v is the image distance (distance of the image from the mirror).
  • The focal length ( f) for a concave mirror is considered negative.
• Given:
  • Radius of curvature (R) = -50 cm (negative for concave mirror)
  • Object distance (u) = -25 cm (negative since the object is on the same side as the incident light for a concave mirror)
  • First, find the focal length using the relationship �=�2 : f = R/2
  • �=(−50cm)2=−25c \({f} = {-50\:cm\over 2} = -25\:cm\) 

Now, substitute the values into the mirror formula:

1(−25)=1(−25)+1�

Solve for v:

\({1\over v} = {1\over -25}-{1\over -25} \)

\({1\over v} = {0}\)

\(\Rightarrow v = \infty\)

This implies that v is at infinity. In the case of a concave mirror, when the image distance (v) is positive infinity, the image is formed at the focus of the mirror.