More about Refraction of Light through a Rectangular Glass_ Proofs of some basic properties and Factors affecting Refraction

 

Go straight, Turn Left, Slight Right and straight again. Finally, you have reached! Welcome! Welcome to the World of Light once again!  I do hope you really enjoyed your previous visit into our mindboggling world. Today we are going to dive deeper in to our renowned town of refraction which is one of the main places scientists choose for adventure sports in our World.

Strap in and get ready for the roller coaster ride as we go through the peculiar effects of a glass slab and different mediums on light.

(If you haven't read the previous blog about the Basics of Refraction of Light and Snell's Law, click on this link ! The Refractive Indices of Light and its relation with the Snell's Law . I would suggest you to read that , before you move ahead in this blog as we will be referring to few concepts from it.)

 

In this blog we will understand why:-

Q) The  Angle of Incidence always equal to the Angle of Emergence in a glass slab?

Q) The Incident Ray and Emergent Ray always Parrallel in a Glass Slab?

and the factors affecting the Refraction of light 

Let's get started! 

The first question we are going to address
Q) Why is the Angle of Incidence always equal to the Angle of Emergence in a glass slab?

We all know (from the previous blog) that 

At X :- μ1 Sin i = μ2 Sin r ( Snell's Law)

At Y :- μ1 Sin e = μ2 Sin r ( Snells Law) 

But ,you might be wondering why both the refraction angles at X and Y are equal ( I am talking about those 2 angles circled in the below picture) 

We know that the two sides of a glass slab is always equal and parallel (as it is a rectuangular/ cuboid structure) , and perpendiculars to parallel lines are also parallel. Hence, If we consider the line XY to be a tranversal , Both the angles of reflection for alternate interior angles (Hence equal!)

As Left Hand side of both the equations are equal we can equate the Right Hand Side (RHS)

u1 Sin i =  u1 Sin e 

So, Angle of Incidence = Angle of Emergence

Q) Why is the Incident Ray and Emergent Ray always Parrallel in a Glass Slab??

Let us extend the emergent ray and incident ray in the above diagram into line L and Line M respectively. 

From the previous section, we saw that Angle of Incidence = Angle of Emergence and Both the angle of Refractions are equal

So Angle A ( Marked by Yellow on line PS) = Angle of Incidence - Angle of Refraction ( By Vertically opposite angles, Angle of Refraction + Angle A = Angle of incidence) 

Similarily

Angle B = Angle of Emergence - Angle of refraction 

As both the RHS are equal , We can equate Left Hand Side

Angle A = Angle B 

And we can see that they actually form alternate interior angles considering XY transversal and LM two lines. 

As Alternate interior angles are equal, Both the lines are parallel!

Incident Ray is Parallel to Emergent Ray

Q) What are the factors the Refraction angle is dependant on?

Here, we have 2 right angles triangles (Green and Yellow)

In triangle Green 

cos r (the top - vertex angle) = thickness / xy

                                            => xy = thickness / cos r  -- 1 eqn

In triangle Yellow

sin (i-r) (the top - vertex angle) = Lateral distance / xy

  Substituting value of xy from 1 eqn     =>  sin (i-r) = d (cos r) / thickness 

Hence

                                                 

From the above equation we can say that the Lateral Shift is dependant on the :-

1) Thickness of slab

2) Angle of Incidence 

3) Refractive Index of the material ( in the above equation , it states that degree of Refraction is dependant on the angle of refraction, which is in direct relation to the refractive indices of the mediums due to the snell's law stated in the previous blog )

4) And also the Colour, wavelength of light 

That's all folks! This marks the end of one of our many rides in this provocative city of refraction, but don't loose hope , there are many more rides coming soon, where we dig deeper into more properties of this peculiar phenomena!