Reflection and Laws of Reflection

Reflection is a very basic process that we come across in day to day life. We can not imagine our life without reflection. Things we are able to see is due to reflection as light rays fall on our eyes through the object and we are able to see. The reason behind the fact that we are able to see our face in the mirror or in the river is reflection. Reflection is also responsible for the echo of sound we hear, it is due to the reflection of sound. Reflection is also used in finding the depth of the oceans. 

From the above paragraph, it is clear that reflection is a very common phenomenon of our life and it is important to study this natural phenomenon for a better understanding of this universe.

Optics is a branch of physics that deals with the phenomenon related to light. It is further divided into two sub-branches: 

• Ray optics: Ray optics is based on rectilinear propagation of light, and deals with mirrors, lenses, reflection, refraction, etc. Ray optics deals with the phenomenon in which light is being treated as a ray mean it cannot bend while travelling.
• Wave optics: Wave optics is a branch in which a wave is associated with light, and it explains phenomena such as diffraction, interference, polarization etc.

Ray optics deals with the phenomenon in which light is being treated as a wave mean it can bend while travelling. Ray optics have further many subtopics like reflection, refraction etc. In this article, we will learn about reflection and its laws.

What is the Reflection of light?

Reflection is natural phenomenon of bouncing back of light rays when it falls on a smooth, shiny surface say mirror. This is what enables us to look at the world around us because light ray which is reflected from these surfaces falls on our retina and this allows us to see.

The light ray which falls down on the mirror is known as the incident ray and the light ray which bounces back from the mirror is known as a reflected ray. The dotted line at the middle is denoted as the normal, which is always perpendicular to the mirror. Normal, incident ray and reflected ray meet at the same point on the mirror.

Reflection

Types of Reflection

Specific reflections create an image. We can observe that the image is inverted as we spin it as if it were reflected from a flat surface. Curved reflections can magnify or demagnify images, hence a curved mirror may have optical power. Spherical or parabolic mirrors, for example, usually have spherical or parabolic surfaces. On this basis, reflections are divided in two as:

• Regular reflection: Regular reflection is a type of reflection that is made through a smooth surface. In this type of reflection, all reflected rays are parallel to each other and all incident rays are also parallel to each other. It follows the laws of reflection. The impression formed by this type of reflection is very bright and clear.

e.g. Reflection through-plane mirror.

• Irregular reflection: Most of the reflections which take place in this universe are reflections from rough and irregular surfaces. Such a type of reflection is called irregular reflection or diffused reflection. In this type of reflection, reflected rays are not parallel provided that incident rays are parallel. The images formed by this type of reflection is distorted and hard to recognize.

e.g. Reflection through the wall.

Irregular reflection

Laws of Reflection

After learning the meaning of reflection, one need to grasp the two laws that govern it. These rules can be used to calculate the incident ray’s reflection on various surfaces such as a plane mirror, water, metal surfaces, and so on. Consider the following laws of reflection in the case of a plane mirror:

Laws of Reflection

• When the light rays falls on the smooth surface, the angle of reflection is equal to the angle of incidence.

For the given case, ∠AOB is the angle of incidence (∠i) and ∠COB is the angle of reflection (∠r) then, according to the first law of reflection, this can be written as:

∠AOB = ∠COB

or 

∠i = ∠r

• The incident ray, the normal and the reflected ray must lie in the same plane.

Hence, in this case, the incident ray AO, the reflected ray CO, and the normal BO to the surface, all lie in the same plane.

Applications of Reflection

• Reflection is used in periscopes to view through the submarines.
• Reflection is the reason why we see objects because the image is formed on our retina and the brain manipulates it through signals.
• Reflection by a concave mirror and a convex mirror has many uses as listed above.
• Reflection property is used in medical fields in diagnosis and optical communications.
• Using the law of reflection for sound and light, we can measure the distances accurately to objects.
• Reflection is the reason why we hear the echo of sound.

Examples of Reflection of Light in daily life

The following are some of the most fascinating examples of light reflection in everyday life:

• The Blue colour of the sky: Because light scatters in all directions when it hits different particles in the atmosphere, the sky is blue. Because blue has a shorter wavelength than red, it scatters more. That is why the sky appears to be blue.
• The Red colour of Sunset: The sunset is red because the sky has already scattered much of the blue light that has travelled around the atmosphere since the day began. As a result, during a Sunset, the red light dominates.
• Clouds look White: Because the water droplets in clouds are significantly larger than the wavelength of light, they appear white. As a result, all of the colours disperse in separate directions to generate white.

Sample Problems

Problem 1: Find the angle of incidence of the light ray, if the angle of reflection is given as 45°.

Solution:

Since, ∠i = ∠r

Therefore, 

∠i = 45°

So, the angle of incidence of light ray is 45°.

Problem 2: Find the angle between normal and reflected ray if the angle between mirror and incident ray is 30°.

Solution:

As we know that mirror and normal are perpendicular to each other.

So, ∠i + angle between mirror and incident ray = 90°

∠i + 30° = 90°

∠i =60°

We know that,

∠i = ∠r

Therefore, 

∠i = 60° 

This implies,

∠r= 60°

So, the angle between normal and reflected ray is 60°.

Problem 3: Two mirrors are situated at an angle of 45° with each other. One light ray is incident on the first mirror at an angle of incidence of 30°. Find the angle of reflection of light through the second mirror.

Solution:

For first mirror,

∠i = 30°

By law of reflection,

∠i  = ∠r

So, ∠r=30°

This reflected ray will act as an incident ray for other mirror. Let the angle of incidence on another mirror be i’ and angle of reflection be r’. A triangle will be formed at the corner with two sides as mirrors and third side as incident cum reflected ray.

First angle = 45°

Second angle = 90° – 30° = 60°

By angle sum property, 

Third angle = 180° – 45° – 60°= 75°

Now, we can easily find the angle of incidence of second mirror.

i’ = 90° – 75°= 15°

By law of reflection,

i’ = r’

So, r’ = 15°

Hence, the angle of reflection through second mirror is 15°.

Problem 4: Find the angle between mirror and reflected ray if the angle between mirror and incident ray is 50°.

Solution:

As we know that mirror and normal are perpendicular to each other.

So, ∠i + angle between mirror and incident ray = 90°

∠i + 50° = 90°

∠i =40°

We know that,

∠i = ∠r = 40°, 

So ∠r = 40°

As we know that mirror and normal are perpendicular to each other.

So, ∠r + angle between mirror and reflected ray = 90°

40° + angle between mirror and reflected ray = 90°

Angle between mirror and reflected ray = 50°

Hence, the angle between mirror and reflected ray is 50°.

Problem 5: If two mirrors are parallel to each other and a light ray is an incident on one of the mirrors with an angle of 35° what will be the angle of reflection after reflecting from the other mirror.

Solution: 

Let the angle of incidence on first mirror be i and angle of reflection be r.

And Let the angle of incidence on another mirror be i’ and angle of reflection be r’ .

i=35°

By law of reflection, 

i = r

So, r = 35°

By simple mathematics, r and i’ form pair of alternate interior angles.

So, r = i’

i’ = 35°

Again, by law of reflection:

i’ = r’

So, r’=35°

Hence, the angle of reflection after reflecting from the other mirror will be 35°.