Multiple choice

A square wire of side $2.0 cm$ is placed $20 cm$ in front of a concave mirror of focal length $10 cm$ with its center on the axis of the mirror and its plane normal to the axis. The area enclosed by the image of wire is

  1. $7.5{ cm }^{ 2 }$
  2. $6{ cm }^{ 2 }$
  3. $2{ cm }^{ 2 }$
  4. $4{ cm }^{ 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mirror formula: 1/v + 1/u = 1/f. u = -20, f = -10. 1/v - 1/20 = -1/10 -> 1/v = -1/20 -> v = -20. Magnification m = -v/u = -(-20)/(-20) = -1. The image is the same size as the object. Area = 2*2 = 4 cm^2.

AI explanation

The mirror formula 1/f = 1/v + 1/u gives the image position as 1/(-10) = 1/v + 1/(-20), meaning 1/v = -1/20 and the image distance is v = -20 cm. The magnification is m = -v/u = 1, which indicates the image is formed at the center of curvature with the exact same dimensions as the object. Therefore, the area enclosed by the square wire's image remains 2.0 cm * 2.0 cm, which equals 4 cm^2. The result is 4 cm^2.

Keep practicing — related questions