Calculating Single Slit Diffraction Width with 630 nm Light

In summary, by using the equations y=Ltan\theta and W = \lambda m / sin \theta, we can calculate the width of a single slit illuminated with 630 nm light and viewed on a screen 2.8 m away. With a linear distance of 12 cm between the first and second dark fringes, the width of the slit is 29.4 micrometers.
  • #1
muffintop
14
0

Homework Statement


A single slit is illuminated with 630 nm light, and the resulting diffraction pattern is viewed on a screen 2.8 m away.
If the linear distance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit?

Homework Equations


y=Ltan[tex]\theta[/tex]
W = [tex]\lambda[/tex] m / sin [tex]\theta[/tex]

The Attempt at a Solution


theta = arctan (.12/2.8) = 2.45
W = 630 x 10^-9 x 2 / sin 2.45
 
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  • #2
Looks good.
 
  • #3
I got 29.4 micrometers. It's wrong though.
 
  • #4
muffintop said:
W = 630 x 10^-9 x 2 / sin 2.45
Oops... I missed that factor of 2 before. Why is it there?

Hint: Write expressions for the first dark fringe position and the second dark fringe position, then subtract.
 
  • #5
I got it thank you so much!
I always get my "m" values wrong.
 

FAQ: Calculating Single Slit Diffraction Width with 630 nm Light

What is single slit diffraction width?

Single slit diffraction width is a phenomenon that occurs when light waves pass through a narrow slit, causing them to spread out and create a diffraction pattern. It is a fundamental principle of wave optics and is commonly observed in experiments with light and other types of waves.

How is the width of a single slit diffraction pattern determined?

The width of a single slit diffraction pattern is determined by the width of the slit and the wavelength of the light passing through it. The narrower the slit and the longer the wavelength, the wider the diffraction pattern will be. This can be mathematically described by the diffraction equation, which takes into account the properties of the slit and the incident light.

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

The intensity of a single slit diffraction pattern is affected by several factors, including the width of the slit, the wavelength of the incident light, and the distance between the slit and the screen or detector. Additionally, the intensity of the pattern can be altered by changing the shape or material of the slit, as well as the angle of incidence of the light.

How is single slit diffraction different from other types of diffraction?

Single slit diffraction is different from other types of diffraction, such as double slit or multiple slit diffraction, because it is caused by a single narrow opening rather than multiple slits. This results in a distinctive diffraction pattern with a central bright spot and alternating dark and light bands on either side.

What are the practical applications of single slit diffraction?

Single slit diffraction has several practical applications, including in optics and spectroscopy. It is used to study the properties of light and other types of waves, as well as to measure the wavelength of light and the size of small objects. It is also utilized in the design of optical instruments, such as telescopes and microscopes, to improve resolution and image quality.

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