Snell’s Law Formula with Solved Example

Snell’s Law Formula

Snell’s Law is used to detect the path taken by a ray of light when it travels between two mediums. This law is used widely in optics to trace the path of light and refractive indexes.

The credit for discovering Snell’s Law goes to Dutch astronomer Willebrod Snell. Although the law was discovered in 1621, it was only after its publication in ‘treatise on the light’ that it became popular.

Snell’s Law states that the ratio of the sine of the angle of incidence to the sine of the angle of reflection is a constant. This means that sin i / sin r = constant. Here i represent the angle of incidence and r denotes the angle of reflection of light. This constant value is equivalent to the ratio of refractive indexes.

The formula for Snell’s Law

 To use Snell’s Law in finding the path of light, we need refractive indexes of two mediums. These are represented by n1 and n2 and their angle of incidence is denoted by a1 and a2.

According to Snell’s Law, the relation between the refractive index and angle of incidence is given by the following formula:

n1/n2 = sin a2/sin a1 

Therefore, if the ratio of the refractive index comes out to be a constant, the ratio of the sine of the angles will also be constant.

How is Snell’s Law derived and what are its common applications?

Snell’s Law is derived from Fermat’s principle, which states that light travels in the shortest path and the time taken in that path is the least time.

Snell’s Law is used widely in optics. For example, it is used in preparing eyeglasses, cameras, rainbows, contact lenses, refractometers, and even in the candy-making industry. This is because it helps us trace the path of the light on the basis of the refractive index.

Solved Examples

Ques 1: If the angle of reflection is 14 degrees and the refractive index is 1.2, what would be the angle of incidence for that medium?

Ans: We know that Snell’s Law states that sin of the angle of incidence divided by sine of the angle of reflection comes out to be constant (i.e. refractive index).

So r= 14, constant= 1.2 and i=? 

Using the formula sin i/sin 14= 1.2 

Sin i= sin 14 (1.2) = 0.28

Therefore i= sin inverse of 0.28.

Ques 2: If I is equal to 25 degrees and R is equal to 32 degrees, what would be the refractive index?

Ans: Sin i/ Sin r = refractive index

Therefore, sin 25/ sin 32= refractive index= 0.797 approx.