Interference and diffraction of light

[poohead]

Homework Statement

green light of wavelength 5000 A is incident normally on a grating, and the 2nd order image is diffracted 32 degrees from the normal. how many lines/cm are marked on the grating

A=10^-10 n= 2 degree= 32 d=? wavelength- 5000 A

the answer to the question is 5300 lines/cm

Homework Equations

wavelength=d sin degree/ n

The Attempt at a Solution

we tried to solve for d using the following above equation but came out with the wrong answer, need help please i am in a fatal situation here,

 

[Doc Al]

we tried to solve for d using the following above equation but came out with the wrong answer, need help please i am in a fatal situation here,

d is the distance between slits, not the number of slits per cm.

 

[poohead]

So then what would I do to get an answer with lines/cm

 

[Doc Al]

So then what would I do to get an answer with lines/cm

Given the spacing between lines, figure out how many fit into a centimeter.

 

[poohead]

the spacing between lines is X?

 

[poohead]

I don't understand then what equation i am to use to solve for such

 

[Doc Al]

I don't understand then what equation i am to use to solve for such

Here's an example: If d = 1/100 of a cm, how many lines are there per centimeter?

 

[poohead]

100? but you said that d is the distance between slits, not the number of slits per cm. so what am i trying to find for this situation?

 

[Doc Al]

100?

Right. If you can do this example, use similar reasoning to solve your problem.

but you said that d is the distance between slits, not the number of slits per cm.

That's true. You use d to calculate the number of slits per cm.

so what am i trying to find for this situation?

Your final answer will be the number of lines per cm. You start by finding d.

 

[poohead]

sorry I am still confused on how to get there, what would i possibly do with d?

 

[Doc Al]

sorry I am still confused on how to get there, what would i possibly do with d?

Try this analogy: Along a path there is a tree every 1/4 mile. How many trees per mile?

Here "1/4 mile" plays the same role as "d".

 

[poohead]

there would be four, but so i solved for d and i get 1.81x10^-6, so now i convert that into cm?

 

[Doc Al]

so i solved for d and i get 1.81x10^-6,

Careful how you round off.

so now i convert that into cm?

Yes, find d in cm.