Interference - Single slit diffraction

In summary, the conversation discusses the application of a single slit diffraction formula to calculate the slit width for monochromatic electromagnetic radiation passing through a slit. The diffraction pattern is observed on a screen at a distance of 2.50 m. After correcting the mistake of using a 2-slit diffraction formula, the correct answer for the slit width is determined to be 4.167x10^-4 m.
  • #1
Isaac Pepper
31
1
< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

Hi guys, I have a question here which I'm struggling to do and perhaps you could help ;

Monochromatic electromagnetic radiation with wavelength λ from a distant source passes through a slit. The diffraction pattern is observed on a screen 2.50 m from the slit.
If the width of the central maximum is 6.00 mm, what is the slit width a if the wavelength is 500 nm (visible light)?

What I have done is

y=(R(m+1/2)lambda) / d where y = 3mm (half of the central maximum width); R = 2.5m m = 0 lambda=500nm

d =( R(m+1/2)lambda) / y

d =( 2.5 * (1/2) * 500x10^-9 )/ 3x10^-3
and so I manage to obtain d = 2.08x10^-4 m, however this answer is wrong

what am I doing wrong?
Thanks !
 
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  • #2
Hello Isaac, welcome to PF :smile: !

This looks an awful lot like homework, so better post it there. You get thrown in a useful template as an extra !

You sure you are applying an equation for a single slit diffraction pattern ?
 
  • #3
I shall do, thanks :)
 
  • #4
Don't re-post; I will move it there now...
 
  • #5
BvU said:
You sure you are applying an equation for a single slit diffraction pattern ?

Thanks ! I have worked it out and I was indeed using the 2-slit diffraction formula :/

The answer was 4.167x10^-4
 
  • #6
Well done ! Hope to see you back some time in the future, but don't hurry...
 

What is interference in the context of single slit diffraction?

Interference is a phenomenon that occurs when two or more waves interact with each other. In the context of single slit diffraction, it refers to the pattern of light and dark fringes that are produced when a single beam of light passes through a narrow slit.

How does a single slit diffraction pattern form?

When a beam of light passes through a narrow slit, it diffracts and spreads out into a wider beam. This diffracted beam then interferes with itself, creating a pattern of bright and dark fringes on a screen placed behind the slit. This pattern is known as the single slit diffraction pattern.

What factors affect the formation of a single slit diffraction pattern?

The formation of a single slit diffraction pattern is affected by several factors, such as the width of the slit, the wavelength of the light passing through it, and the distance between the slit and the screen. A wider slit will produce a narrower pattern, a shorter wavelength will create a wider pattern, and a longer distance between the slit and the screen will create a larger pattern.

How is the intensity of the fringes in a single slit diffraction pattern determined?

The intensity of the fringes in a single slit diffraction pattern is determined by the degree of interference between the diffracted waves. The bright fringes occur where the waves are in phase and reinforce each other, while the dark fringes occur where the waves are out of phase and cancel each other out.

What are some real-life applications of single slit diffraction?

Single slit diffraction has many practical applications, such as in optical filters, where the pattern of fringes can be used to selectively filter out specific wavelengths of light. It is also used in spectrometers to analyze the composition of light sources, and in diffraction gratings to produce highly accurate measurements of wavelengths of light.

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