track spacing

kujan · Post by **kujan** » Thu Oct 19, 2006 10:12 am

Please help me derive the formula for track spacing...d(sin Î¸m - sin Î¸i ) = mÎ»...i need it urgently as my project is due next week....Thank you...

johnsteele · Post by **johnsteele** » Thu Oct 19, 2006 12:04 pm

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

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

kujan · Post by **kujan** » Thu Oct 19, 2006 12:09 pm

I already have that link...the formula used in the experiment (d(sin Î¸m - sin Î¸i ) = mÎ»)...i want to know how its derived...Thank you

johnsteele · Post by **johnsteele** » Thu Oct 19, 2006 12:40 pm

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

kujan · Post by **kujan** » Thu Oct 19, 2006 12:44 pm

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

ghariman · Post by **ghariman** » Thu Oct 19, 2006 12:47 pm

Hi Kujan,

The equation that you are as asking of:
d(sin Î¸m - sin Î¸i ) = mÎ»
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.

kujan · Post by **kujan** » Thu Oct 19, 2006 12:55 pm

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...

ghariman · Post by **ghariman** » Thu Oct 19, 2006 12:59 pm

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.

kujan · Post by **kujan** » Thu Oct 19, 2006 10:56 pm

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

kujan · Post by **kujan** » Thu Oct 19, 2006 10:59 pm

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

Louise · Post by **Louise** » Fri Oct 20, 2006 7:16 am

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

kujan · Post by **kujan** » Fri Oct 20, 2006 7:20 am

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

Louise · Post by **Louise** » Fri Oct 20, 2006 8:30 am

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

kujan · Post by **kujan** » Fri Oct 20, 2006 8:33 am

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

KUJAN

Louise · Post by **Louise** » Fri Oct 20, 2006 8:36 am

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

KUJAN

Glad it is clear. Good luck with the math!

Louise