What is the Separation of Two Apertures in a Light Diffraction Grating?

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SUMMARY

The discussion focuses on calculating the separation of two apertures in a light diffraction grating, specifically for a light source with a wavelength of 600nm. The user seeks clarification on using the equation dsinθm = mλ to find the aperture separation (d) given the parameters L = 2m and Y = 5cm. The correct order number (m) for the second order intensity maximum is confirmed to be 2, not 0. This establishes the necessary relationship between path difference and wavelength for accurate calculations.

PREREQUISITES
  • Understanding of light diffraction principles
  • Familiarity with the equation dsinθm = mλ
  • Knowledge of wavelength measurement in nanometers
  • Basic trigonometry related to angles in physics
NEXT STEPS
  • Review the derivation of the diffraction grating formula dsinθm = mλ
  • Explore the concept of path difference in wave interference
  • Learn about the significance of order maxima in diffraction patterns
  • Practice problems involving aperture separation calculations in light diffraction
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Students studying optics, physics educators, and anyone interested in understanding light diffraction and interference patterns.

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Homework Statement


A source of light shines through two apertures resulting in an intensity distribution pattern on a viewing screen.

The central bright fringe is called the m=0 or zeroth order maximum.

In the schematic diagram 1, the light source is to the left of the page and the point P represents the position of the second order intensity maximum on the screen. Two rays r1 and r2 are depicted incident at P.

Calculate the separation d of the two apertures, given the wavelength of the light is 600nm, L = 2m, Y = 5cm.
Remember that δ is the path difference between the rays (vectors) r1 and r2.

Hint: We need to be able to relate δ to the order number and the wavelength of the light.



Homework Equations


Diagram_1.png


Diagram_2.png


The Attempt at a Solution


From wikipedia it says that dsinθm = mλ
I assume I need mλ to find out separation d of the two apertures.
λ = 600nm, L = 2m, Y = 5cm
m = 0
I'm not sure how to comprehend the wavelength.
I really need someone to explain what I need to do here.
Any help would be grand!
 
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Check you understand what "m" is in this equation..

dsinθm = mλ

Then check what value "m" is when...

point P represents the position of the second order intensity maximum
 
Ahh second order, I had m = 0 which is zeroth order.
So m should equal 2?
 

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