Question

What can be the largest distance of image of a real object from a convex mirror of radius of curvature 20cm.
 $
  \left( {\text{A}} \right)10cm \\
  \left( {\text{B}} \right)20cm \\
  \left( {\text{C}} \right){\text{infinity}} \\
  \left( {\text{D}} \right){\text{zero}} \\
  $

Answer 1

Hint :Start the solution by defining what is a convex mirror. Since the convex mirrors have reflecting surfaces on the outside of the sphere, the focal point and the curvature are on the inside. Hence first try to find out the focal length of the mirror with the help of radius of curvature which will be the largest distance from the convex mirror.

Complete Step By Step Answer:
A convex mirror has a spherical reflecting surface. The source of the light is faced by the bulging side of the mirror. The image obtained on the convex mirror is always virtual, diminished and upright. The distance between the object and convex mirror is measured at a distance where the image reflection reaches an approximate size of the object.
Image is only formed between the focus and mirror in a convex mirror.
The focal length of the convex mirror is given by $ f = \dfrac{R}{2} $ where R is the radius of curvature of the convex mirror.
Hence the maximum distance will be $ f = \dfrac{{20}}{2} = 10 $
Hence the maximum distance will be 10cm.
Hence the answer to our question is option (B) 10cm.

Note :
Since the focal point is on the opposite side of the mirror from the object, the focal length is negative for a convex mirror. But since we were asked about the distance we have considered a positive value as distance is never negative. Convex mirrors are widely used in day to day life uses.