Angle of Incidence

Angle of incidence is the angle created between a ray propagating on a surface and the line normal to the point of occurrence on the same surface. The manner in which the light is reflected back to the observer after it strikes a mirror is an excellent demonstration of how reflection works.

In this article, we will learn more about what the angle of Incidence is, the formula for the angle of incidence, examples related to the angle of incidence, the difference between the angle of incidence and the angle of reflection, and some of the frequently asked questions related to it.

What is Angle of Incidence?

At the point of incidence, two angles are formed by the incident ray and the reflected ray, viz., the angle of incidence and the angle of reflection.

👁 Angle-of-Incidence-(1)

• The angle of incidence is the angle formed by a ray of light striking a surface of contact and the normal drawn at the point of incidence.
• The angle of reflection is the angle created at the point of incidence between the normal and the reflected ray.
• The first line involved in the angle of incidence is the incident light ray that strikes a surface. At the point where the incident ray touches the surface, a normal is drawn.
• As per the law of reflection, the angle of incidence is equal to the angle of reflection, i.e. ∠i = ∠r.

Angle of Incidence-Formula

We can calculate the angle of incidence by using the following equation from the Snell's Law:

👁 Angle-of-Incidence-Formula

,

where

• ?_i is angle of incidence
• ?_r is angle of refraction
• n₁ is refractive index of the medium through which light ray is coming from
• n₂ is refractive index of the medium through which light ray is going into

Note: If both the mediums are same, then n₁ = n₂.

Since, we know that the angle of incidence is equal to the angle of reflection (according to the law of reflection), the angle of reflection can be easily calculated once angle of incidence is known.

Example of Angle of Incidence

Suppose you have been standing on a beach enjoying the view of the ocean. The sun is directly overhead.

• The sun's light beams are striking the water at an angle of incidence.
• The angle formed by the light rays and the water's surface is known as the angle of incidence.
• The angle of incidence and reflection are equal in this particular case.
• This suggests that the angle at which light beams strike the water will also be the angle at which they reflect off of it. You will thereby be able to see the sun's reflection in the water.

Angle of Incidence and Angle of Refraction

The relationship between the angles of incidence and refraction is explained through Snell's law (which is known as the law of refraction), which states that the ratio of the sine of the angle of refraction and angle of incidence is always constant and equal to the ratio of phase velocities of the two mediums it is passing through.

• When a ray of light passes through one medium to another it gets deviated. We refer to this phenomenon as the refraction of light.

👁 Angle-of-Incidence-and-Angle-of-Refraction

• The angle of incidence is the angle created at the point of incidence between the incident ray and the normal.
• The angle of refraction is the angle that forms between the refracted ray and the normal.
• Angle of Incidence and angle of refraction lie in different media.

Read More

• Reflection of light
• Total Internal Reflection
• Refraction of light

Solved Problems on Angle of Incidence

Example 1. Find the angle of incidence and the angle of reflection for the ray of light striking the plane reflecting surface at 60°.

👁 Angle-of-Incidence-example-1

Solution:

Angle of incidence = 90°- 60° = 30°

As we know that, angle of incidence = angle of reflection,

Therefore, Angle of reflection = 30°

Hence, the angle of reflection for the ray of light striking the plane reflective surface at 60° is 30°.

Example 2. A ray of light strikes the plane reflective surface at an angle of 57. Calculate:

👁 Angle-of-Incidence-example-2

(i) The angle of incidence (i)

(ii) The angle of reflection (r)

(iii) The angle created by the reflected ray and the surface (q).

(iv) The angle formed between the incident ray and the ray that is reflected from the surface.

Solution:

From the diagram drawn above,

The angle of incidence = 90° - 57° = 33°

According to the law of reflection, the angle of incidence = the angle of reflection. Hence,

⇒ ∠r = ∠i = 33°

The angle created between the reflected ray and the reflective surface can be calculated as,

⇒ ∠q = 90 - ∠r = 90° - 33° = 57°

Now, the angle between the incident and the reflected rays = 33° + 33° = 66°