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

In summary, the conversation discusses the concept of intensity distribution patterns created by a source of light shining through two apertures. It mentions the central bright fringe, known as the m=0 or zeroth order maximum, and provides a schematic diagram showing the light source and the position of a second order intensity maximum on the viewing screen. The task is to calculate the separation d of the two apertures using the given values of wavelength, distance, and Y. The equation dsinθm = mλ is referenced and it is determined that in this case, m should equal 2.
  • #1
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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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  • #2
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
 
  • #3
Ahh second order, I had m = 0 which is zeroth order.
So m should equal 2?
 

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

What is a light diffraction grating?

A light diffraction grating is an optical component that is used to separate light into its component wavelengths. It consists of a large number of evenly spaced parallel lines or grooves on a reflective surface, which cause light to diffract and produce a spectrum.

How does a light diffraction grating work?

A light diffraction grating works by causing light to diffract as it passes through the parallel lines or grooves. Each groove acts as a tiny slit, and the diffracted light from each slit interferes with the light from other slits, creating a pattern of bright and dark spots known as a diffraction pattern. This pattern can be used to analyze the different wavelengths of light present in the original beam.

What are some applications of light diffraction gratings?

Light diffraction gratings have many applications in science and industry. They are commonly used in spectroscopy to analyze the chemical composition of substances, in telecommunications to separate different wavelengths of light for fiber optic communication, and in optical instruments such as cameras and telescopes to improve image quality.

What is the difference between a reflection grating and a transmission grating?

A reflection grating reflects light off its surface, while a transmission grating allows light to pass through it. Both types of gratings produce a diffraction pattern, but the spacing and orientation of the lines or grooves may differ. Reflection gratings are typically used for shorter wavelengths of light, while transmission gratings are more suitable for longer wavelengths.

Can light diffraction gratings be manufactured with different properties?

Yes, light diffraction gratings can be manufactured with different properties such as varying groove spacing, angle, or material. These properties can affect the diffraction pattern produced and the range of wavelengths that can be diffracted. Customizable gratings can be designed for specific applications or to produce a desired diffraction pattern.

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