Answer to Question #269226 in Optics for NICKO

Question

A pencil that is 9.0 cm long is held perpendicular to the surface of a plane mirror with the tip of the pencil lead 12.0 cm from the mirror surface and the end of the eraser 21.0 cm from the mirror surface. What is the length of the image of the pencil that is formed by the mirror? Which end of the image is closer to the mirror surface: the tip of the lead or the end of the eraser?

Answer 1

Length of the pencil is 9 cm.

Distance of the surface of a plane mirror with the tip of the pencil lead is 12.0 cm.

Distance of the surface of a plane mirror with the end of the eraser is 21.0 cm.

The characteristics of the plane mirror are:

- The size of the image formed in the plane mirror is precisely equal to the size of the object in front of the mirror. The magnification of the plane mirror is zero. For example, if a 1 m tall boy is standing in front of the plane mirror than the image formed behind the mirror is also 1 m long.

- Plane mirrors only reflect the object in the opposite direction with no change in object distance, the distance of an object from the surface of the mirror will be equal to the distance of the image from the surface of the plane mirror but in the opposite direction.

Therefore, the length of the image of the pencil formed by the mirror is also 9 cm long, with no change in size.

In object point of view tip of the lead is closer to the surface of the plane mirror with a distance of 12 cm, Therefore, in image point of view tip of the lead is closer to the surface of the plane mirror with a distance of -12 cm.