Inteference of light ray in thin flim

[desmond iking]

Homework Statement

according to the notes in the photo, the light ray undergo of phase change of 0.5 λ when it strike and reflected from glass surface (denser) at point A . so the OPD of ray 1 &2 = 2nt-0.5λ..
but in the 2nd photo , the OPD of ray 1 & 2 is given by 2nt+0.5λ . i am not sure which one is correct. can someone enlighten me on this?

Homework Equations

The Attempt at a Solution

 

[BvU]

Well well, you've really gone out of your way to make life easy for us poor helpers...

Now all we need is some relevant equations and your attempt at a solution, right ?

 

[desmond iking]

Sorry. I don't umderstand the situation so I hope someone can help me out on this.

 

[desmond iking]

Or should I post this problem in other section? Which section should I post?

 

[ehild]

Homework Statement

according to the notes in the photo, the light ray undergo of phase change of 0.5 λ when it strike and reflected from glass surface (denser) at point A . so the OPD of ray 1 &2 = 2nt-0.5λ..
but in the 2nd photo , the OPD of ray 1 & 2 is given by 2nt+0.5λ . i am not sure which one is correct. can someone enlighten me on this?

They are equivalent. The electric field changes to the opposite when reflected from the surface of a higher index material. The phase change can be taken either pi or -pi, all the same. (If you add pi or - pi to the argument of a sine function, you get the same: sin(x+pi) = sin(x) cos (pi) = -sin(x) and sin(x-pi)= sin(x)cos (-pi) = -sin(x) as cos(pi)=cos(-pi)=-1.) They correspond to optical path differences +λ/2 or -λ/2.
I would prefer 2nt+0.5 λ for the optical path difference, so as it is positive even with very thin layers.

ehild

 

[desmond iking]

They are equivalent. The electric field changes to the opposite when reflected from the surface of a higher index material. The phase change can be taken either pi or -pi, all the same. (If you add pi or - pi to the argument of a sine function, you get the same: sin(x+pi) = sin(x) cos (pi) = -sin(x) and sin(x-pi)= sin(x)cos (-pi) = -sin(x) as cos(pi)=cos(-pi)=-1.) They correspond to optical path differences +λ/2 or -λ/2.
I would prefer 2nt+0.5 λ for the optical path difference, so as it is positive even with very thin layers.

ehild

hi, please refer to the photo 2 . It is shown that the n start from 1 , but not 0 .
If the n start form 0 , the thickness surely will become negative value. which is indeed wrong.( from mathematical treatment)
I can't understand why the n can't be start from 1 from the physics theory. can you explain on this?

 

[ehild]

according to the notes in the photo, the light ray undergo of phase change of 0.5 λ when it strike and reflected from glass surface (denser) at point A . so the OPD of ray 1 &2 = 2nt-0.5λ..
but in the 2nd photo , the OPD of ray 1 & 2 is given by 2nt+0.5λ . i am not sure which one is correct. can someone enlighten me on this?

You asked if the OPD (optical path difference) can be written as 2nt-0.5λ or 2nt+0.5λ. In that context, n is the refractive index and t is the thickness of the layer.
If you use μ to denote the refractive index, you should write the OPD as 2μt-0.5λ.

If you mean the condition of constructive interference, the optical path difference should be integer multiple of λ, 2μt-0.5λ=kλ or 2μt=(k+0.5)λ, k=0, 1,2,...

In case the OPD is taken 2μt+0.5λ, the condition of constructive interference is 2μt=(k-0.5)λ, k=1,2,...ehild

 

[desmond iking]

If you mean the condition of constructive interference, the optical path difference should be integer multiple of λ, 2μt-0.5λ=kλ or 2μt=(k+0.5)λ, k=0, 1,2,...

In case the OPD is taken 2μt+0.5λ, the condition of constructive interference is 2μt=(k-0.5)λ, k=1,2,...


ehild

why for
2μt=(k-0.5)λ , the k starts from 1 but can't be 0 ? can you explain it using physics theory?

 

[ehild]

t, the layer thickness would be negative at k=0, which is impossible.

ehild

 

[desmond iking]

t, the layer thickness would be negative at k=0, which is impossible.

ehild

i knew this (from maths) , but can you explain in 'physics way' ?

 

[ehild]

Have you seen anything with negative thickness? For example how would a -0.2 m thick wall look like ?

ehild