An object is placed in front of a concave mirror of focal length f, and it is found that an image of the same size as that of the object is formed. The object distance u is: 

The correct answer is equal to 2f.

Key Points

• For a concave mirror, when the object is placed at a distance equal to the radius of curvature (2f), the image formed is of the same size as that of the object.
• The image formed in this case is real, inverted, and of the same size as the object.
• This is derived from the mirror formula and the magnification equation for concave mirrors.
• According to the mirror equation: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
• For an image to be the same size as the object, the object distance u must be equal to 2f.
• This scenario is a classic case of image formation by concave mirrors used in optics problems.

 Additional Information

• Concave Mirror
  • A concave mirror is a spherical mirror that curves inward like a portion of the interior of a sphere.
  • It can form real and virtual images, depending on the position of the object.
  • It is often used in applications like reflecting telescopes, makeup mirrors, and headlights of vehicles.
• Focal Length
  • The focal length (f) is the distance between the mirror's surface and the focal point.
  • It is half of the radius of curvature (R), i.e., f = R/2.
  • Focal length is a crucial parameter in determining the image formation properties of the mirror.