2 parallel rays are travelling in a medium

[zorro]

Homework Statement

2 parallel rays are traveling in a medium of refractive index 4/3. One of the rays passes through a parallel glass slab of thickness t and refractive index 3/2. What will be the path differnce between the two rays due to the glass slab?

The Attempt at a Solution

The optical path covered by the ray inside the glass slab equals the phase difference.
So x=3/2 x t

The answer is incorrect.

 

[sigmaro]

Dear AbdulKadir, that is easy;
l=nx right?
for first one l=(4/3)t
for second one l'=(3/2)t
path difference is (1/6)t, don't get confused, other is not traveling at space it also in a medium

 

[Sourabh N]

Phase difference would be the difference in optical paths. One ray goes through a medium of r index 3/2, other through 4/3. Find the optical paths and subtract.

 

[zorro]

AbdulKadir

l=nx right?
for first one l=(4/3)t
for second one l'=(3/2)t
path difference is (1/6)t, don't get confused, other is not traveling at space it also in a medium

The first ray doesnot travel through the glass slab. How did you write 4/3t?

Phase difference would be the difference in optical paths. One ray goes through a medium of r index 3/2, other through 4/3. Find the optical paths and subtract.

So do you mean the answer will be (1/6)t?

 

[Sourabh N]

Yes.

 

[zorro]

Sorry that answer is incorrect.

 

[Sourabh N]

A trivial problem - We have assumed c = 1. Does the answer assume that too?

A not so trivial problem - The refractive index of glass slab wrt the surrounding medium is (3/2) / (4/3) = 9/8. So the path difference would be 9/8 * t - t = 1/8 * t. This makes more sense to me because the background medium is not air (with r index 1), but a medium with r index 4/3. Does it make sense to you?

 

[zorro]

You are correct now.
But I didnot understand one thing, why did you subtract t from 9/8*t ?

 

[Sourabh N]

9/8 * t is the optical path through the glass slab (placed in water), t is the optical path in water. Path difference = Subtract them.

In other words, the same reason we subtracted 4/3 * t earlier.

 

[zorro]

Thanks!