Snells Law

Concept Explanation

Snells Law

This law say that the ratio of sine of angle of incidence to the sine of angle of refraction is constant for a pair of media i.e

. $frac{sin;i}{sin;r}= constant(_1eta_2 )$

where $large _1eta_2$ is the refractive index of the medium 2 w.r.t. medium 1.

Application of Snell's Law:

Ray Falling Perpendicular to Surface:

The ray which falls perpendicular to the refracting surface goes into the second medium undeviated.. This phenomenon can be explained with the help of Snell's law. As the ray is falling perpendicularly so the angle of incidence is 0

$angle ;i = 0^0$

From Snell's law we get

$frac{sin;i}{sin;r}= constant(_1eta_2 )$

$sin;r= frac{sin;i}{_1eta_2 }$

Now $sin;i= sin;0^0 = 0$

So $sin;r= frac{0}{_1eta_2} = 0$

$sin;r= sin; 0^0$

$Rightarrow r = 0^0$

As the angle of refraction is 0 so the ray goes without deviation.

Optically Denser and Rarer Medium:

In the pair of transparent medium, the medium that has a higher refractive index is called a denser medium and the other is called a rarer medium.

When light passes from rarer to denser medium it slows down and bends toward the normal as shown in the figure R denotes rarer medium and D denotes denser medium.

Using Snells law:

$eta _1;sin;theta_1 =eta _2;sin;theta _2 Rightarrow frac{sin;theta _1}{sin;theta _2}=frac{eta _2}{eta _1}$

As the ray is moving from optically rarer medium to optically denser medium so

$large eta _2> eta _1$

Angles are inversely proportional to refractive index, we get

$large theta _2< theta _1$

Hence light bends towards the normal

When light passes from denser to rarer medium the speed increases and it bends away from the normal as shown in the figure R denotes rarer medium and D denotes denser medium.

Using Snells law:

$eta _1;sin;theta_1 =eta _2;sin;theta _2 Rightarrow frac{sin;theta _1}{sin;theta _2}=frac{eta _2}{eta _1}$

As the ray is moving from optically denser medium to optically rarer medium so

$large eta _2< eta _1$

Angles are inversely proportional to refractive index, we get

$large theta _1< theta _2$

Hence light bends away from the normal

Light Propagating Through A series of Different Medium:

When light propagates through a series of layer of different medium, then

$mu _1sinphi _1=mu _2sinphi _2=mu _3sinphi _3=..........=constant$

Proof: Let us take the case of three layers of Medium 1 with refractive index $eta_1$ , Medium 2 with refractive index $eta_2$ , Medium 3 with refractive index $eta_3$ and Medium 4 with refractive index $eta_4$ as shown in the figure below

Case I : Light rays goes from medium 1 to medium 2 where angle of incidence is $phi_1$ and angle of refraction is $phi_2$ . Then according to Snell's law

$frac{sin; phi_1}{sin;phi_2}= frac{eta_2}{eta_1}$

$Rightarrow ;;eta_1 times sin; phi_1= eta_2 times sin;phi_2$ ........[ I ]

Case II : Light rays goes from medium 2 to medium 3 where angle of incidence is $phi_2$ and angle of refraction is $phi_3$ . Then according to Snell's law