Science Buddies: "Ask an Expert"

Please help me derive the formula for track spacing...d(sin θm - sin θi ) = mλ...i need it urgently as my project is due next week....Thank you...

I'm not sure for what you are asking, but this might help.

https://www.sciencebuddies.org/mentorin ... p011.shtml

I already have that link...the formula used in the experiment (d(sin θm - sin θi ) = mλ)...i want to know how its derived...Thank you

You might what to look at derivations of Bragg's law.

could you please send me a link...or type out the derivation...it would be really helpful....

Hi Kujan,

The equation that you are as asking of:
d(sin θm - sin θi ) = mλ
is called the "Grating Equation".

Below is a website that I found that has the derivation of the equation:
http://scienceworld.wolfram.com/physics ... ating.html

Here is a very good explanation of the grating equation with many pictures. In particular look at figures 1, 2 and 4:
http://www.lot-oriel.com/site/site_down ... s_deen.pdf

Hope this helps. When reading the derivation make sure to understand each step of it and not just use it blindly.

Thanks a billion George...this is very useful information...dont know wat i would have done otherwise...thanks again

KUJAN

p.s. I am an ISC student (12th grade) from India. This experiment is part of my internal assessment for my board exam. So i owe u big time...

kujan wrote:Thanks a billion George...this is very useful information...dont know wat i would have done otherwise...thanks again

KUJAN

p.s. I am an ISC student (12th grade) from India. This experiment is part of my internal assessment for my board exam. So i owe u big time...

Hi Kujan,

All the best for your project then.

Mr. George,

i went through the links carefully as you asked me to. I do not understand how the 4th equation is obtained...could you please explain it to me...Thanks

also...the 6th and the 7th equations...shouldnt it be a1 and a2 respectively?

kujan wrote:Mr. George,

i went through the links carefully as you asked me to. I do not understand how the 4th equation is obtained...could you please explain it to me...Thanks

These derivations just use simple geometry. Look closely at the figures, and the equations, and you should see how these are derived. What does each side of the equation #4 look like? (What formula?) How does that relate to the diagram of a triangle?

Louise

I got #4...Thanks...but what about the other 2....how do you explain that...

kujan wrote:I got #4...Thanks...but what about the other 2....how do you explain that...

Well, looking at the page, they say you need to solve the 4 equations for the 4 unknowns. So the first 4 equations are the obvious geometrical constraints that you get by looking at the pictures.

(Obviously, if you look at the picture, you would get exactly what you proposes d1 and a1 should be related by the angle of the small triangle.)


So, you need to solve for d1 and d2 in terms of a (not a1 or a2) using the 4 equations above.


Louise

excellent...now its crystal clear....thanks a lot...Louise

KUJAN

kujan wrote:excellent...now its crystal clear....thanks a lot...Louise

KUJAN

Glad it is clear. Good luck with the math!

Louise