How Do Grating Lines and Wavelength Affect Diffraction Patterns?

[physicoo]

Hi guys, I currently have a few doubts with diffraction grating (mostly theoretical-wise), so minimal calculations are involved.

I basically did an experiment on diffraction grating, involving looking through a diffraction grating and observing the spectra, aiming a laser beam at the grating etc.

What I would like to clarify is:

1) Suppose a grating with more lines per unit length (meaning the grating constant d, decreases) is used, I assume the angles and spread of spectra both increase, mainly due to the grating equation of d.sin(theta) = m(lambda)?

2) Now suppose the wavelength of light used is increased (E.g. From green to red), similarly to the previous question, I am again assuming the angles and spread of spectra also increases, again due to the grating equation.

3) I understand that there is a limit to the order of spectrum that can be observed in diffraction grating, and I've read that it's primarily because the angle theta cannot exceed 90 degrees, so the limit of the order is mainly (grating constant/wavelength). Could anyone explain to me why it can't exceed 90 degrees?

Appreciate the help! :)

 

[Liquidxlax]

you have to find what would be constant. Like are you viewing a single value of m with a certain diffraction grating. So then theta and lambda are proportional.

I do remember this lab from first year physics and that is how i thought of it. We were viewing m= 1, 0, -1 and you know that 0 always is constant while the position of 1 and -1 change based on the wavelength as long as the grating is constant.For the 90 degree thing, how does light go behind a grating? The only way would be by reflections, so light cannot exceed an angle greater then parallel to its source

Hope that helps

 

[physicoo]

Yes, I've thought of that too. Which is how I derived my stand from the equation of d.sin(theta) = m(lambda).

Say, in regards to the first question, if d decreases, and the wavelength and m is held constant, I find the angles increase (in fact, quite significantly). And same goes for the spread of the spectra, after having calculated the result, which also increases when d decreases.

Cheers! :)

 

[Liquidxlax]

Yes, I've thought of that too. Which is how I derived my stand from the equation of d.sin(theta) = m(lambda).

Say, in regards to the first question, if d decreases, and the wavelength and m is held constant, I find the angles increase (in fact, quite significantly). And same goes for the spread of the spectra, after having calculated the result, which also increases when d decreases.

Cheers! :)

you are quiet right sir :)

 

[physicoo]

Thanks :)

As for the third question, is anyone able to explain to me why the angle is unable to exceed 90 degrees? I do not understand what would happen, if it exceeds.

 

[rl.bhat]

θ is the angle between the diffracted ray and the normal. When θ = 90 degrees, the diffracted rays graze the plane of the grating. Hence θ cannot be more than 90 degrees.

 

[physicoo]

Yup, I've read up on other sites and realized the reason why it can never exceed 90 degrees :) Thanks though!

I've got a last question though it's somewhat a little more of I-just-wanna-know-why. When holding the diffraction grating to my eye and looking at light sources, I saw multiple images of the light source, in different colors (not sure if I'm supposed to see this though!). I am assuming this is due to the grating (kind of obvious) which 'diffracts' the light into a spectrum of colors which was observed.

But how exactly does the grating piece give this kind of effect when we look through it? I'm thinking it's somewhat related to the multiple colors we see when we hold the disc under a light source.

 

[rl.bhat]

Diffraction depends on the wavelength of the light source. when a white light passes through the grating, just like a prism, different colors come out of the grating in different direction.

 

[physicoo]

So I suppose this diffraction grating piece basically acts like a prism, 'spreading out' the light into its component colors, one of which end has the highest wavelength while the other end has the lowest wavelength?

 

[rl.bhat]

So I suppose this diffraction grating piece basically acts like a prism, 'spreading out' the light into its component colors, one of which end has the highest wavelength while the other end has the lowest wavelength?

Yes. But the order of the colors are reversed in the spectrum.

 

[physicoo]

Think I understand now :) Thank you!