2.2 Reflection by a plane mirror

  Reflection of Light

• The focal length and radius of curvature of plane mirror are infinite.
• The image formed by the plane mirror is at the same perpendicular distance behind the mirror as the object is in front of it.

• The image formed by the plane mirror is laterally inverted.

• The image formed by the plane mirror is always erect, virtual and of same size as the object.

• Intensity of image formed by larger mirror is more as the image is formed from more numbers of reflected rays.
• If the mirror moves away or towards an object by a distance $d$, then the image moves away or towards the object by a distance $2d$.

• Also, if the mirror moves with speed $v$ towards or away from a fixed object, then image appears to move towards or away from the object with speed $2v$.
• If the object moves with speed $v$ towards a fixed mirror, the image also moves towards the mirror with speed $v$. The speed of the image relative to the object in this is $2v$.
• When a plane mirror is rotated through an angle $\theta $ keeping the incident ray fixed, then the reflected ray rotates by an angle $2\theta $ in the same direction.

• The minimum length of a plane mirror to see full height $h$ of a person in the mirror is $\left( {\frac{h}{2}} \right)$. The mirror has to be placed in a fixed position.

• When a man is standing exactly midway between a wall and a mirror. If he wants to see the full height $h$ of the wall behind him in the plane mirror in front of him, the minimum length of mirror has to be $\left( {\frac{h}{3}} \right)$.

As $\Delta \;ACE$ and $\Delta \;CHG$ are similar. So, $$\begin{equation} \begin{aligned} \frac{{{h_1}}}{b} = \frac{x}{{2x}} \\ {h_1} = \frac{b}{2} \\\end{aligned} \end{equation} $$

Similarly, $\Delta \;FDB$ and $\Delta \;HDI$ are similar. So, $$\begin{equation} \begin{aligned} \frac{{{h_2}}}{a} = \frac{x}{{2x}} \\ {h_2} = \frac{a}{2} \\\end{aligned} \end{equation} $$

Height of the mirror is given by, $$h_m = \left( {\frac{{a + b}}{2}} \right)\quad ...(i)$$

From the figure, $$\begin{equation} \begin{aligned} h = a + b + {h_m} \\ h = (a + b) + \left( {\frac{{a + b}}{2}} \right) \\ h = \frac{3}{2}(a + b)\quad ...(ii) \\\end{aligned} \end{equation} $$

From equation $(i)$ and $(ii)$ we get, $${h_m} = \frac{h}{3}$$

• When two plane mirrors are inclined at angle $\theta $ and an object is placed between them, then the number of images of an object are formed due to multiple reflections.

The number of images formed is given by, $$n = \frac{{360^\circ }}{\theta }$$

• Field of view of an object for a given mirror
  

A mirror what ever may be its size, it forms the image of all objects lying in front of it. But every object has its own field of view for the given mirror.

The field of view is the region between the extreme reflected ray and depends on the location of the object in front of the mirror. If our eye lies in the field of view then only we can see the image of the object otherwise we cannot see.

The field of view of an object placed at different locations in front of a plane mirror is as shown in the figure.