Angle of Incidence: Formula, Example, Diagrams and Sample Questions

The angle of incidence refers to the angle that is formed between the normal, which is the line that is formed perpendicular to the incident point, and the incident ray of light. This is an important concept of reflection of light. In this article, we will explore the definition and formulas of the angle of incidence and its relation with the angle of reflection.

Key Terms: Angle of incidence, angle of refraction, angle of reflection, incidence, refraction, reflection, light, ray of light, incident ray, reflected ray

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What is the Angle of Incidence?

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The angle that a ray of light makes with the normal drawn at the point of incidence when it falls on a surface of contact is known as the angle of incidence. When a path of a ray of light collides with a line parallel to an interface, it forms the angle of incidence. The angle produced by the normal and the ray of light is called the angle of incidence.

In the same way, the angle that is formed between the reflected ray and the normal at the point of incidence is known as the angle of reflection.

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Key Concepts

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When a ray of light is reflected on a surface, it reflects back at an angle equal to the angle of incidence.

• The ray of light that first hits the surface to be reflected further is known as the incident ray.
• The incident ray hits the surface at a point known as point of incidence with a certain angle that is called the angle of incidence.
• A line that is drawn perpendicular to the point of incidence is known as a normal.
• The ray of light that is reflected back after hitting the surface is known as the reflected ray.

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Formula of Angle of Incidence

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The rule of reflection states that the angle of incidence equals the reflected angle. Hence, the angle of incidence and reflection are always the same, and they are in the same plane as normal.

• ∠i = ∠r 
• The angle of incidence = 900 - the angle the ray of light makes with the surface.

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Example of Angle of Incidence

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• When a seismic wave collides with strata, it forms an acute angle. The angle of incidence is 0, the wavefront is parallel to the surface, and the path of the ray is perpendicular, or normal, to the contact in normal incidence.

• The angle that is formed by a ray of sunlight colliding with a line perpendicular to a surface; for example, a surface directly facing the sun has an angle of incidence of 0, whereas for a surface parallel to the sun (like rays of the sun striking a horizontal rooftop) has an angle of incidence as 90°. Sunlight with a 90° incidence angle is absorbed, while light with a lower angle is reflected.

The insolation of the sun varies at different places on Earth due to its varying angle of incidence 

• The angle created between a ray propagated on a surface and the line normal to the point of occurrence on the same surface is known as the angle of incidence. When a ray of light strikes a mirror's surface, it reflects back to the source.

Angle of Incidence

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Relation between Angle of Incidence and Angle of Refraction 

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Snell's law states that the ratio of the sine of the angle of refraction to the sine of the angle of incidence is always constant and equivalent to the ratio of phase velocities of the two mediums it is passing through, describing the relationship between the angle of incidence and angle of refraction.

A ray of light strikes the flat surface of a mirror. From the incident point, the same ray is refracted. The point is divided by a perpendicular, which splits both angles. The angle of incident ray and angle of refracted ray can be related using the normal.

The angle of incident ray and angle of refracted ray

The ray of light makes contact with two different mediums. The first is a more scarce medium, whereas the second is a denser medium. When compared to the speed of light in the denser medium, the rarer medium has a faster speed. The medium has a significant influence on the angle of incidence and refraction. 

Air or any other type of gas is an example of a rarer medium. Denser mediums include glass, diamonds, and kerosene. The speed of light is slowed inside the denser medium, but there is no resistance to the speed of light from any rarer medium.

The angle of incidence can be calculated by using Snell's Law.

According to this law:

\(\frac{sin\theta}{sin\phi} = \frac{n_2}{n_1}\)

where,

θ = angle of incidence

Φ = angle of refraction

n₁ = the incident medium's index

n₂ = the refracting medium's index.

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Things to Remember

• The point of incidence is the location where light strikes a surface. The normal is a line that is drawn perpendicular to that location.
• The angle that a ray of light makes with the normal drawn at the point of incidence when it falls on a surface of contact is known as the angle of incidence.
• ∠i = ∠r 
• Snell's law states that the ratio of the sine of the angle of refraction to the sine of the angle of incidence is always constant and equivalent to the ratio of phase velocities of the two mediums it is passing through.

\(\frac{sin\theta}{sin\phi} = \frac{n_2}{n_1}\)

• The angle of deviation decreases as the angle of incidence rises, and when it reaches a point where the angle of incidence equals the angle of emergence, the angle of deviation is at its minimum, and it will begin to decrease again.
• The angle of reflection is the angle created at the point of incidence between the normal and the reflected beam.

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