Solve Diffraction Grating Homework: Freq, Spacing, Angle

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Homework Help Overview

The discussion revolves around a diffraction grating problem involving calculations for grating spacing, angle of diffraction, and frequency of light. The original poster presents a series of calculations related to these aspects, specifically focusing on the number of lines per meter in the grating and the wavelength of light.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate grating spacing and the angle of the first order using the formula dsin=nλ, while questioning whether to convert units from nanometers to meters. They also explore the relationship between speed, frequency, and wavelength.

Discussion Status

Participants provide feedback on the calculations, noting mathematical errors and the importance of unit conversion. Some guidance is offered regarding the use of the inverse sine function and the necessity of including units in answers. The discussion reflects a collaborative effort to clarify and correct the original poster's approach.

Contextual Notes

There is an ongoing discussion about unit conversions, particularly converting wavelengths from nanometers to meters, and ensuring that calculations are presented with appropriate units. The original poster expresses uncertainty about their calculations and seeks confirmation on their methods.

jendrix
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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
 
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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
 
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
 
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.:wink:
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
 
Excellent, really appreciate the help:smile:
 
:zzz:so the units are ?
 
:smile:Sorry it's Hz
 

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