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Snell's Law Formula

Snell's Law is about how light rays alter its direction when it travels from one medium to the other. When light travels from one medium to other it undergoes refraction. The ratio of the sines of the angles of incidence and refraction is constant for all incidences in any given pair of media for electromagnetic waves of a definite frequency when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. This law of refraction (Snell's law) states that :
  • The incident ray i, the refracted ray r and the normal N for the given surface at a point of incidence lies in the same plane
  • For any pair of medium, the sine angle of incidence i to the sine angle of refraction r ratio is constant ($\mu$).

Snells Law Example

Snell's law formula for the given pair of media is given by

Snells Law Formula
Where, $\mu$ is the refractive index value of second medium with respect to first called as n21.

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Snell's Law Examples

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Lets see some examples on Snell's law:

Solved Examples

Question 1: If a ray is incident at an angle of 20o and the refractive index is 1.4. Calculate the refracted angle.
Solution:
 
Given: Incident angle i = 20o, refractive index $\mu$ = 1.4
The refracted angle is given by

$\frac{sin\ i}{sin\ r}$ = $\mu$

$\frac{sin\ 20}{sin\ r}$ = 1.4

sin r = $\frac{0.34}{1.4}$
r = sin-1(0.2428) = 140 3'
r = 14o 3'.


 

Question 2: If a ray refracts at an angle of 320 and the refractive index is 0.8. Calculate the incident angle.
Solution:
 
Given: Refracted angle r = 320, refractive index $\mu$ = 0.8

The refracted angle is given by

$\frac{sin\ i}{sin\ r}$ = $\mu$

$\frac{sin\ i}{sin\ 32}$ = 0.8

sin i = 0.8 $\times$ 0.5299
i = sin-1 (0.4239) = 25o 4'
i = 25o 4'.

 

More topics in Snell's Law Formula
Critical Angle Formula
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