Reflection On A Plane Mirror - Practice Questions & MCQ

\Object: Objects are sources of light rays that are incident on an optical element.

• Real object: An object is real if two or more incident rays actually emanate or seem to emanate from a point. 
• Virtual object: An object is virtual when two incident rays seem to converge to that point.

 Image: An image is the point of convergence or apparent point of divergence of rays after they interact with a given optical element. An object provides rays that will be incident on an optical element. The optical element reflects or refracts the incident light rays which then meet at a point to form an image. As in the case
of objects, images too can be real or virtual.

•  Real Image: Real images are formed when the reflected or refracted rays actually meet or converge to a point. If a screen is placed at that
  point, a bright spot will be visible on the screen. Thus, a real image can be captured on a screen. 
• Virtual image: an optical image formed from the apparent divergence of light rays from a point, as opposed to an image formed from their actual divergence

Image formation by plane mirror: 

We have to see the rays coming from the object to see it. If the light first hits the mirror and then reflects with the same angle, the extensions of the reflected rays are focused at one point behind the mirror. We see the coming rays as if they are coming from behind the mirror. At a point, A' image of the point is formed and we call this image a virtual image The distance of the image to the mirror is equal to the distance of the object to the mirror.

a) For a point object 

 Distance of object from mirror = Distance of image from the mirror

(i) All the incident rays from a point object after reflection from a plane mirror will meet at a single point which is called an image. 

(ii) The line joining a point object and its image is normal to the reflecting surface 

b) For an extended object :

The size of the image is the same as that of the object. An image of an extended object by a plane mirror is a virtual image. The image will be upright and laterally inverted.

Rotation of plane mirror

i)  Mirrror is rotated keeping ray of incidence fixed: 

Consider that before the mirror is rotated the angle of incidence and recfection is $\theta$. When the mirror is rotated through and angle of say $\phi_{\text {in a clockwise direction, then the normal is also rotated by an angle } \phi}$ and thus the new angle of incidence becomes $\theta+\phi$ and thus new angle of reflection will be to $\theta+\phi$ as shown in the below figure.

So the angle between the incident ray and new reflected ray is $2(\theta+\phi)$..........
Let due to rotation of mirror new reflected ray get deflected by an angle $\delta$ in a clockwise direction with respect to the original reflected ray.

So So the angle between the incident ray and the new reflected ray is $2 \theta+\delta$. from the equation (1) and (2) we get $\delta=2 \phi$
i.e For fixed incident ray, When the mirror is rotated $\phi$ in a clockwise direction then reflected ray get deflected by $2 \phi$ in the clockwise direction

ii)  Mirror is fixed, angle of incident ray  changed : 

when the mirror is fixed and the angle of incidence is changed by an angle   in an anti-clockwise direction, Then the angle of reflection will rotate by  an angle    in the clockwise direction as shown in the below figure.



The angle of Deviation - 

The angle of Deviation is the angle made by the reflected ray with the direction of the incident ray.

A ray of light (PO) that is incident on to the surface of a plane-mirror is reflected as OR with the angle of incidence equal to the angle of reflection. Suppose that the ray had continued, through the mirror, in a straight line along OQ as shown in the below figure.  

Then the angle made by the reflected ray (OR) with OQ is called the angle of Deviation ()

As for the above figure

$
\begin{aligned}
& i+r+\delta=\pi \\
\Rightarrow & \delta=\pi-i-r \quad(\text { and } u \operatorname{sing} i=r) \\
\Rightarrow & \delta=\pi-i-i=\pi-2 i
\end{aligned}
$
 

Number of images formed by two plane mirrors

Number of images formed by two plane mirrors: 

 The number of images formed by two adjacent plane mirrors depends on the angle between the mirror. If θ (in degrees) is angle between the plane mirrors then the number of images are given by,

                                                  $n=\frac{360}{\theta}-1$

                                            n = no. of images formed

Let us take few cases(with some condition) to understand it better -

Case 1: When two mirrors are placed parallel to each other

When the two mirrors are aligned at a 0-degree angle with each other (i.e., a parallel mirror system), there is an infinite number of images. The diagram below shows the multiple images for a parallel mirror system. Images I₁ and I₂ are primary images. Image I₁ is the image resulting from the reflection of the object O across mirror M₁ and image I₂ is the image resulting from the reflection of the object O across mirror M₂. Image I₃ is an image of image I₁, found by reflecting image I₁ across mirror M₂. Image I₄ is an image of image I₂; found by reflecting image I₂ across mirror M₁. This process could continue indefinitely, producing images of images for an infinite number of images extending to the right of mirror M₂ and to the left of mirror M₁. we can also calculate number of images formed by using formula

where  is 0 degrees. So the number of images formed will be infinite.

Case 2: When two mirrors are placed perpendicular to each other

The number of images formed when two mirrors are placed at an angle theta to each other is given by:

$
n=\frac{360}{\theta}-1
$

So, here, we have the mirrors placed perpendicular to each other. So, $\theta=90$ degree

$
\begin{aligned}
n & =\frac{360}{90}-1 \\
n & =4-1 \\
n & =3
\end{aligned}
$
 

Case 3: When two mirrors are placed at 120 degrees 

Here, we have the mirrors placed at an angle of 120 degrees. and object is kept at angle bisector of two mirrors. So, $\theta=120$ degrees.

$
\begin{aligned}
& n=\frac{360}{120}-1 \\
& n=3-1 \\
& n=2
\end{aligned}
$

Also when the object is not kept at angle bisector of two mirrors then the number of images formed by two mirrors can be calculated by the formula

$
\begin{aligned}
& n=\frac{360}{\theta} \\
& n=\frac{360}{120} \\
& n=3
\end{aligned}
$

- If the value of $\frac{360}{\theta}$ is even, then we will use the formula

$
n=\frac{360}{\theta}-1
$

360
But If the value of $\frac{360}{\theta}$ is odd, then we have two different cases
1. $n=\frac{360}{\theta}-1 \quad \ldots$ (when the object is placed symmetrically)
2. $n=\frac{360}{\theta} \quad \ldots$ (when the object is placed asymmetrically)