Reflection of Light at Plane Surface

The branch of physics which deals with the phenomena of light is called optics. A ray of light is the path along which the lights travel. That is, the ray of light gives the direction along which the light energy travels. Rays are visible. They travel along the straight line in the same homogeneous medium and are represented by straight lines with arrow heads. The arrow head indicates the direction of light. A collection of a large number of rays is called a beam of light. A beam of light may be parallel, convergent or divergent as shown in the figure.

Reflection of Light at Plane Surface

Light rays are basically wave motions and they are capable of being reflected by an interface in between two mediums. The phenomenon of coming back to the light in the same medium when it falls on a surface is known as the reflection of light. The surface which reflects back the light is called a reflecting surface. Reflection of light obeys certain laws known as laws of reflection.

Laws of reflection

When a ray of light is incident on a plane mirror, it follows following laws:

1. The incident ray, the reflected ray and the normal at the point of incidence lie on the same plane.
2. The angle of incidence is equal to the angle of reflection.

A ray of light AO is incident at point O on the surface of the mirror and gets reflected along OB. ON be a normal drawn at point O on the surface. It if found that the incident ray AO, reflected ray OB and the normal ON at the point of incidence all lie in the same plane. This is a vertical plane which is normal to the plane of the mirror. Again, ÐAON = i, angle of incident and ÐBON = r, the angle of reflection. Then i = r as shown in the figure.

When a beam of light is incident on a smooth surface, the reflected beam has the same angle of reflection which is called regular reflection. However, when the beam of light is incident on a rough surface, the reflected rays have a different angle of reflection which is not equal to the angle of incidence which is called irregular reflection.

Deviation of Light by Plane Mirror

Glancing angle is made by an incident ray with reflecting surface. Its value in a mirror varies from 0^o at grazing incidence to 90^o at the normal incidence.

Let us consider a plane mirror XY. When a ray of light AO is incident at point O on the surface of the mirror with glancing angle Ï´, the ray is reflected along OB as shown in the figure. NO is a normal drawn at point O.

AOC is the path of the incident ray before reflection and OB is the path of reflection. The angle \(\delta\) between the paths of incident ray and reflected ray is called the angle of deviation. We can write, angle of deviation, \(\delta\)=∠BOC = ∠BOY + ∠YOC

\begin{align*} \text {or,} \: \delta &= 90 – r + \theta \\ \text {or,} \: \delta &= 90 – i + \theta \\ &= \theta + \theta \\ \therefore \delta &= 2\theta \\ \end{align*}

Thus the angle of deviation of a ray by a plane mirror is equal to the twice of the glancing angle.

Deviation of Reflected by Rotating a Mirror: Law of Rotation of Light

The law of rotation of light states that “when a mirror rotates through an angle Ï´, then the reflected rotates through angle 2Ï´.”

Let us consider a plane mirror XY as shown in the figure. When a ray of light OA is incident at a point O on the surface of the mirror with glancing angle α, the ray is reflected along OB. Then the deviation suffered by the reflected is

$$\angle BOC = 2\alpha \dots (i) $$

Suppose the mirror is rotated through an angle Ï´ on keeping incident ray fixed, the reflected ray then rotates along OB’ through an angle β. So, the deviation suffered by the reflected ray with rotation of the mirror is

\begin{align*} \angle B’OC &= 2(\alpha + \theta ) \\ \text {Now the angle of deviation} \\ \angle B’OB &= \angle B’OC - \angle BOC \\ &= 2(\alpha + \theta ) – 2\alpha = 2\theta \\ \beta &= 2\theta \\ \end{align*}

Image Formed by a Plane Mirror

Let us consider a plane mirror XY and a point object is placed at point O. rays of light coming from the object is incident on the plane mirror at point A and C at different angles of incidence and are reflected along AB and CD respectively. A normal incidence E is reflected normally.

All these reflected rays are seen in the eye on coming from point I as shown in the figure I is the position of a virtual image and it is in equal distance with object from the mirror, OE = EI. This can be proved as follows:

\begin{align*} \text {From the laws of reflection of light, we have} \\ \angle OAN &= \angle NAB \\ \text {or,} \: i &= r \dots (i) \\ \text {Again, we can write} \\ \angle OAN &= \angle EOA = i \dots (ii) \: (\therefore \text {Alternate angles }) \\ \text {and} \: \angle NAB &= \angle AIE = r \dots (iii) \: (\therefore \text {Corresponding angles }) \\ \text {From equation} \: (i), \: (ii) , \text {and} \: (iii), \: \text {we have} \\ \angle EOA &= \angle AIE \dots (iv) \\ \text {Thus from} \: \Delta s \: \text {OEA and EIA, we have} \\ \angle EOA &= \angle AIE \\ \angle OEA &= \angle IEA \: (\therefore \text {both are right angles} ) \\ EA &= EA \: (\therefore \text {common arms} ) \\ \text {So these two triangles are congruent and} \: OE = EI \\ \end{align*}