Snell’s Law Formula: Definition, Refractive Index, Sample Questions

Snell's Law is another name for the formula that describes refraction. Light is partly reflected and partly refracted when it strikes a smooth barrier between two transparent materials (transmitted). The angle of refraction is determined by the light's angle of incidence and the two materials' indices of refraction. A material's index of refraction is determined by its qualities. Snell's Law always measures angles in relation to the barrier's normal, which is perpendicular to the barrier's surface. The indexes of refraction are unitless values, while the angles are measured in radians or degrees.

Key Takeaways: Incident angle, Refraction angle, Refractive index, Light, Refraction, Reflection, Snell's Law, glass

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What is Snell’s law?

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Consider an incident ray coming from air and hitting the surface of glass. We know that the incident ray will always bend towards the normal in this case.

Let the incident angle i = 30° and angle of refraction r = 19.5° (Refer below figure)

Air is one medium and glass is another medium.

The speed of light is high in air and the speed of light is low in the glass. Due to this change in speed, light is refracted.

So, optically air is rarer medium and glass is denser medium.

Let’s say

Refractive index of air is n₁ = 1,

What will be the refractive index of glass n₂ = ?

We can guess that the refractive index of glass will be greater than 1. Beacuse glass is a more optically denser medium.

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Snell’s Law Formula

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Consider a light source of a bulb and a material like glass. Let the bulb produce light in all directions. An incident ray of light hitting the surface of the glass, is the point of incidence. The incidence ray is travelling from Air medium to glass medium.

Air is a rarer medium and glass is a denser medium.

Light travel bent towards normal in denser medium like glass.

First case,

Now, let the angle of incidence i is 30° in the air.

The angle of refraction r = 19.5° in the glass medium.

Second Case,

An incident ray is travelling from air to glass.

Let, the angle of incidence i be 60° in air and angle of refraction r = 35.5° in the glass.

Third Case,

Consider one last case in which an incident ray is travelling from air to water.

Let the incident ray i = 50° and angle of refraction r = 36°

Here, Snell's law states that the ratio of the sine of the angle of incidence to the sine of angle of refraction remains constant until medium is the same.

For Example:

In the first case the angle of incident angle is 30° and the angle of refraction is 19.5°.

So, sin 30°/sin 19.5° = 1.5

In the second case the angle of incident is 60° and the angle of refraction is 35.5°.

So, sin 60°/sin 35.5° = 1.5

In the third case, the incident angle is 50° and angle of refraction is 36°.

So, sin 50°/sin 36° = 1.3

Snell's Law accurately states that the ratio of the sin of the angle of incidence to the sin of angle of refraction is constant until the medium remains the same.

In the first case the ratio is 1.5, in the second case the ratio is 1.5 and third case ratio is 1.3.

In the third case the ratio is not the same because in the first and second case light is entering into the glass, so, the sin ratio of incident angle and refracted angle remains constant. While in the third case the light is entering into a different angle like in water. Thus the sin angle of incident and refracted angle remains constant until the medium is the same.

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What is Refractive Index?

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The value which we get in all the above cases is known as the refractive index. Refractive index indicates the speed of light in different media. It is denoted by ‘n’. When refractive index is greater than the speed of light is slower.

How can we find refractive index of glass? Here we use Snell’s Law, Sin angle of incidence and refracted angle remains constant is equal to refractive index

Sin i/sin r = constant

Now, instead of this constant put the refractive index of air and glass in the Snell’s law

So, sin i/sin r = n₂/n₁ (first method)

Second method

Divide the above diagram into two parts

The upper part and the lower part is

n₁sini = n₂sinr (second method)

Now, what is refractive index of glass?

Plug in all the values in Snell’s law

1 × sin30° = n₂ sin19.5°

n₂ = 1.5

Refractive index of glass would be greater than the refractive index of the air

Snell’s Law is studied to:

1. To find the angle of incidence
2. To find the angle of refraction
3. To find refractive index

Also Read:

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Things to Remember

• Snell's law states that the ratio of the sine of the angle of incidence to the sine of angle of refraction remains constant until medium is the same.
• The refraction of a wave travelling from one medium to another or from a gradual change in the medium is the change in direction of the wave.
• The light that falls on an object is known as incident light. It can come from a natural source, such as the sun, or from a man-made source. Incident light is light that bounces off another surface, such as a reflector.
• When light travels through two different mediums with two different indices of refraction, Snell's Law yields the equation that indicates how light is refracted.