If an object is placed in front of a concave mirror at a distance of 20 cm and the image is formed on the same side at a distance of 40 cm, then the magnification of the mirror will be: 

The correct answer is -2.

Key Points

• The magnification (m) of a mirror is calculated using the formula: m = -v/u, where 'v' is the image distance and 'u' is the object distance.
• Here, the object distance (u) is -20 cm (negative as it is in front of the mirror) and the image distance (v) is -40 cm (negative as it is a real image formed on the same side as the object).
• Substituting the values, m = -(-40 cm) / (-20 cm) = 40 / 20 = 2.0.
• Since the image is real and inverted, the magnification will be negative: m = -2.0.
• Thus, the correct magnification of the mirror is -2.0, which corresponds to option 4.

Additional Information

• Concave Mirrors:
  • Concave mirrors are spherical mirrors that curve inward, resembling a portion of the interior of a sphere.
  • They are known to converge light rays to a focal point, making them useful in applications like telescopes and shaving mirrors.
• Mirror Formula:
  • The mirror formula relates object distance (u), image distance (v), and focal length (f) through the equation: 1/f = 1/u + 1/v.
• Magnification:
  • Magnification (m) indicates how much larger or smaller the image is compared to the object.
  • For mirrors, it is calculated as the ratio of the image height to the object height or -v/u for distances.
• Real vs. Virtual Images:
  • Real images are formed when light rays converge and can be projected on a screen; they are inverted.
  • Virtual images occur when light rays only appear to diverge from a point; they are upright.