Solve Diffraction Grating Homework: Freq, Spacing, Angle

[jendrix]

Homework Statement

The number of lines per metre in a grating is 500,000, calculate grate spacing.

The wavelength of light going through the grating is 600nm, what is the angle of the first order?

What is the frequency of the light is it's speed is 3 x 10^8 m/s?

Homework Equations

The Attempt at a Solution

For 1 I did 1/500,000 giving 2 x 10^6 m/s

2)Using dsin=nλ

I rearranged to give sin = 600/2 x 10^6 which gave me 0.861

Should I have converted the 600 into metres and used 6x10^-7?

3) Using c=fλ

3x10^8 = f x 600

f = 500,000 Again should I have converted the 600nm into meters?Thanks for looking

 

[technician]

You are on the right track but you have made mathematical mistakes.
1/500000 is 2x10^-6
You must change nm into m
Hope this helps

 

[jendrix]

Thank you, so for no 1 I have

1/500,000 = 2 x 10^-6


2)sin =6 x 10^-7 / 2 x 10^-6

This gives 0.3 but should this be multiplied by inverse sin to give 17.48?


3) 3 x 10^8 / 6 x 10^-7 = 5 x 10^14

Do these look ok?

Thanks

 

[technician]

In part 2 you have calculated that Sin∅ = 0.3 so yes!... you need to use the inverse Sin function on your calculator to find the angle Make certain that you have your calculator set to
degrees not radians.
In part 3 you have not given any units... you must do this to produce a complete answer.
Other than these details you are OK

 

[jendrix]

Excellent, really appreciate the help

 

[technician]

:zzz:so the units are ?

 

[jendrix]

Sorry it's Hz