Application of the properties of light

[Paige]

Homework Statement

Light with wavelengths of 520 nm and 630 nm passes through a diffraction grating that contains 6000lines/cm.
a) Sketch a diagram of the image produced from m = 0 to m = 2. Label the order of each fringe.
b) Calculate the angles for the first and second order maxima that would appear on the screen.
c) What is the lowest value of m for which the 520 nm line no longer exists? Justify your answer.
d) Compare the appearance of the fringe at m=0 with all the others.

Homework Equations

SinΘ= mΛ/d
d= 1m/6.0x10^5lines
d=1.67x10^-6m/line

The Attempt at a Solution

I am taking a learn at home course and this material is very new to me. I don't want to be told answers I'm just having a lot of difficulty grasping the entire concept of light if I'm being honest.
I have used the equation to solve for b and c.
The issue I'm having, perhaps I am over thinking it, is that I do not know how to sketch the diagram of the maxima and fringes. How am I to know the distances between fringes and the maxima? I tried to look through other equations in previous chapters but they require another variable, L, which I do not have. Of course without the sketch I cannot solve D.
I was just hoping someone could help guide me into figuring it out on my own.

 

[Simon Bridge]

The issue I'm having, perhaps I am over thinking it, is that I do not know how to sketch the diagram of the maxima and fringes.

Just draw what you'd expect to see on a screen. If you don't know what that is, you should look for some pictures of diffraction patters online.

How am I to know the distances between fringes and the maxima?

That's what the equations are for.
You may want to use a little geometry - but your notes should have that done for you.
However you don't need to know to draw a sketch. You just need to illustrate the important points.

I tried to look through other equations in previous chapters but they require another variable, L, which I do not have. Of course without the sketch I cannot solve D.

You don't need to be so exact. It's only a sketch to give the idea.

 

[mfb]

How am I to know the distances between fringes and the maxima? I tried to look through other equations in previous chapters but they require another variable, L, which I do not have.

All distances will scale in the same way with L. For a sketch, you don't need exact distances, the scale can be arbitrary.

 

[BvU]

Hello Paige, welcome to PF :)

This is a physics subject that can be nicely supported with internet stuff like here
Google double-slit interference to find a ton more sites. Wikipedia has a nice animated picture.
Hyperphysics is a good site too.

 

[Paige]

Just draw what you'd expect to see on a screen. If you don't know what that is, you should look for some pictures of diffraction patters online.

That's what the equations are for.
You may want to use a little geometry - but your notes should have that done for you.
However you don't need to know to draw a sketch. You just need to illustrate the important points.

You don't need to be so exact. It's only a sketch to give the idea.

I know what diffraction patterns look like but to sketch a diffraction pattern with two different wavelengths and label both maxima is what is throwing me off.
Am I on the right track if I use my calculations for part B to help me locate the m0-2 on the sketch? As the angles for the first and second orders are different could I assume that would affect their distance to the central maximum? the 520nm wavelength, for example, is 18degrees at m1 where as the 630nm wavelength is 22 degrees.
So, to sketch I would assume that means the 520nm would have a m1 closer to the central maximum?
Of course doing this I feel the sketch is very vague and won't be scaled correctly.

 

[Simon Bridge]

You can do it for either one?
The combined pattern is the sum of the two by themselves.
Have you seen the diffraction pattern for white light?