Snell's law and optical filters.

[Greger]

Hi,

I recently did a experiment in which I measured the intensity of light out of a optical filter at different angles of incidence.

The optical filter was designed such that only light of wavelength 405 nm is transmitted. The wavelength of incident light (the laser I used) was 402 nm.

My first measurement was 0 degree's which meant the laser was perpendicular to the filter. I obtained an intensity peak at 10 degree's which had a width of around 10 degree's. So the intensity at 0 and 20 degrees was small.

Now I was asked to calculate the band-width. I think I can do this using Snell's rule.

$\frac{sin(\theta_1)}{sin(\theta_2)} =\frac{\lambda_1}{\lambda_2}$

I know that at 10 degree's the wavelength into the filter is 402 nm and the wavelength inside it 405 nm (since all of the light is transmitted) so I can calculate the angle of refraction (I get 10.075).

My question is, how can I calculate the wave length light inside the filter at angles 0 and 20 degrees (when the intensity drops)?

At first I was thinking that I could keep the angle of refraction constant, then just substitute the new angle of incidence in and calculate the wavelength inside, but I know that's not right (the angle of refraction wouldn't be constant).

I was wondering, would the difference between the angle of incidence and refraction be the same? Like for the incidence angle 10, the angle of refraction is 10.075 so the difference is 0.075. Would this be the same for the incidence angle 20? If so then it's possible to calculate the wavelength inside the medium with incidence angles 0 and 20, but if not, I'm not sure how else I could do it as I wouldn't know the angle of refraction.

Thank you

 

[UltrafastPED]

Here is some information on optical filter testing:
http://semrock.com/Data/Sites/1/semrockpdfs/whitepaper_measurementofopticalfilterspectra.pdf

and http://www.photonics.com/Article.aspx?AID=25446

Note that there is more than one way to make a pass band filter, and this will affect your model. This is discussed in more detail in the second article.

 

[Greger]

Thanks for your reply,

I am required to determine the band width using the method I described in my first post.

The second article you posted does show similar results to what I have obtained, however I am asking how, from the information I currently have, can I calculate λ₂. (Recall the information I have is the incident angle and wavelength, I am not sure about the angle of refraction)

 

[Enigman]

I don't know if I am correct but:-

...I know that at 10 degree's the wavelength into the filter is 402 nm and the wavelength inside it 405 nm (since all of the light is transmitted) so I can calculate the angle of refraction (I get 10.075).

You can get the refractive index of the fibre by this and then and use it to calculate angle of refraction.

My question is, how can I calculate the wave length light inside the filter at angles 0 and 20 degrees (when the intensity drops)?

Wavelength of light depends only on the speed of light in the medium and shouldn't be affected by either angle of incidence or intensity.

I was wondering, would the difference between the angle of incidence and refraction be the same?

Nope, that doesn't make any sense to me. Their ratio on the other hand should be constant (refractive index).
Hope this helps.

 

[Nickie]

for sharing your experiment and question about Snell's law and optical filters. Snell's law is an important principle in optics that describes the relationship between the angle of incidence and refraction when light passes through a medium with a different refractive index. In your experiment, the optical filter is designed to only transmit light of a specific wavelength, 405 nm. When the incident light has a wavelength of 402 nm, some of the light will be transmitted through the filter while the rest will be reflected or absorbed.

To calculate the bandwidth of the filter, you can use the formula you mentioned, \frac{sin(\theta_1)}{sin(\theta_2)} =\frac{\lambda_1}{\lambda_2}, where \theta_1 is the angle of incidence and \theta_2 is the angle of refraction. However, in order to calculate the angle of refraction for different incident angles, you will need to know the refractive index of the filter material. This can be determined experimentally by measuring the angles of incidence and refraction for a known wavelength of light.

Once you have the refractive index, you can use Snell's law to calculate the angle of refraction for different incident angles. The difference between the angle of incidence and refraction will not be the same for all angles, but you can use this information to calculate the wavelength of light inside the filter at different angles. This can be done using the formula, \frac{sin(\theta_1)}{sin(\theta_2)} =\frac{\lambda_1}{\lambda_2}, where \theta_1 is the angle of incidence and \theta_2 is the angle of refraction.

In summary, to calculate the bandwidth of the filter, you will need to determine the refractive index of the filter material and use Snell's law to calculate the angle of refraction for different incident angles. This will allow you to calculate the wavelength of light inside the filter at different angles and determine the width of the transmission peak. I hope this helps and good luck with your experiment!