Optics - index of refraction and phase lag

In summary: AB/λ0) = (n-1)(10mm/500nm) = 20(n-1) In summary, The number of extra cycles in 1 mm of glass compared to 1 mm of free space is 20 times the difference between the index of refraction and 1.
  • #1
atomqwerty
94
0

Homework Statement



A light beam of wavelenght 500nm travels from A to B in vacuum. (AB = 10mm)
If we put a glass sheet with n=1.5 and 1mm thick, calculate how change the number of periods. Calculate the phase lag too.


Homework Equations



k0 = 2Pi/λ (vacuum)

k= k0·n

The Attempt at a Solution



If in the vacuum the wave gas a wavelenght λ=2Pi/k0, into a n=1.5 glass, it will have λ'=2Pi·n/k0 (?)

Thanks
 
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  • #2
Yes, that's correct.
 
  • #3
How many more waves are there in 1 mm of glass than there are in 1 mm of free space?
 
  • #4
SammyS said:
How many more waves are there in 1 mm of glass than there are in 1 mm of free space?

If the wavelenght is λ, in a free space of d=1mm there will be k=λd waves, and in d'=1mm glass (index n) there will be k'=λnd', so if we put the glass into de space d, this leads to

k=λ(d-d')

k'=λd'n

therefore the number of waves (total) will be

K = k+k'

Is this correct?

thanks
 
  • #5
No, you didn't calculate the number of cycles correctly. Both λ and d have units of length, so using your expression, k would have units of length squared. The number, however, should be unitless.

(k isn't the best letter to use since k is typically used to denote the spatial frequency.)
 
  • #6
vela said:
No, you didn't calculate the number of cycles correctly. Both λ and d have units of length, so using your expression, k would have units of length squared. The number, however, should be unitless.

(k isn't the best letter to use since k is typically used to denote the spatial frequency.)

If k = 2Pi/λ [meters^(-1)], then kd, with [d=meters] is unitless, isn't it?

Thanks
 
  • #7
vela said:
(k isn't the best letter to use since k is typically used to denote the spatial frequency.)

Ok, my mistake, but is K = k+k' as we define k and k' [uniteless] the number of waves?
 
  • #8
SammyS said:
How many more waves are there in 1 mm of glass than there are in 1 mm of free space?

The number of waves in a thickness d of glass, is: d/(λ) = d/(λ0/n) = nd/λ0, where λ0 is the wavelength in a vacuum.

So, the number of EXTRA cycles is: nd/λ0-d/λ0 = (n-1)(d/λ0)
 

FAQ: Optics - index of refraction and phase lag

What is the index of refraction?

The index of refraction is a measure of how much the speed of light is reduced when it passes through a medium, compared to its speed in a vacuum. It is represented by the symbol "n" and is calculated by dividing the speed of light in a vacuum by the speed of light in the medium.

How does the index of refraction affect the path of light?

The index of refraction determines the angle at which light bends as it passes through a medium. This bending, known as refraction, is due to the change in speed of light. The higher the index of refraction, the more the light will bend.

What factors affect the index of refraction?

The index of refraction is affected by the density and composition of the medium, as well as the wavelength of the light passing through it. Generally, denser materials have a higher index of refraction, and shorter wavelengths of light are more strongly refracted than longer wavelengths.

What is phase lag in optics?

Phase lag is the difference in the phase between two points on a wave. In optics, it refers to the difference in the timing of oscillations between two points on an electromagnetic wave. This can be caused by factors such as differences in the speed of light in different media.

How is the index of refraction related to phase lag?

The index of refraction is directly related to phase lag in optics. This is because the index of refraction determines the speed of light in a medium, which in turn affects the wavelength and frequency of the light. A change in the index of refraction will result in a change in the phase of the wave, leading to phase lag.

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