Help With Simple Single Slit Diffraction Pattern?

In summary, the problem involves plane light waves incident on a single slit of width 2.45 cm, where the second dark fringe is observed at an angle of 44.3° from the central axis. Using the equation θ=pλ/a, where θ is in radians, p=2, and a= slit width, the attempt at a solution involved solving for the wavelength (λ) by substituting the values and converting degrees to radians. The resulting unit for the wavelength may be in nanometers or meters.
  • #1
bmb2009
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Homework Statement


Plane light waves are incident on a single slit of width 2.45 cm. The second dark fringe is observed at 44.3° from the central axis. What is the wavelength of the light?


Homework Equations


θ=pλ/a... where theta is in radians, p =2 (second light minimum), and a = slit width

this seems like it should be a simple problem but I can't get the answer..any Help?


The Attempt at a Solution


I tried

44.3°=.7732 rad so .7732=(2)(λ)/.0245 and solved for λ. Also, does come out in nano meters or meters?

Thanks for your help!
 
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  • #2
bmb2009 said:

Homework Statement


Plane light waves are incident on a single slit of width 2.45 cm. The second dark fringe is observed at 44.3° from the central axis. What is the wavelength of the light?


Homework Equations


θ=pλ/a... where theta is in radians, p =2 (second light minimum), and a = slit width

this seems like it should be a simple problem but I can't get the answer..any Help?


The Attempt at a Solution


I tried

44.3°=.7732 rad so .7732=(2)(λ)/.0245 and solved for λ. Also, does come out in nano meters or meters?

Thanks for your help!

That is a very wide slit if you are expecting to notice diffraction of light.!
 

1. What is a simple single slit diffraction pattern?

A simple single slit diffraction pattern is a phenomenon in which a single slit is illuminated by a narrow beam of light, and the resulting pattern of diffraction is observed on a screen behind the slit. This pattern is characterized by a central bright fringe, surrounded by a series of increasingly dimmer, alternating bright and dark fringes.

2. How does a single slit diffraction pattern form?

A single slit diffraction pattern forms when light waves pass through a narrow slit and diffract, or spread out, as they pass through the slit. This causes the light to interfere with itself, creating a pattern of bright and dark fringes on a screen placed behind the slit.

3. What factors affect the appearance of a single slit diffraction pattern?

The appearance of a single slit diffraction pattern is affected by several factors, including the wavelength of the light, the width of the slit, and the distance between the slit and the screen. These factors determine the spacing and intensity of the fringes in the pattern.

4. What is the significance of a single slit diffraction pattern?

A single slit diffraction pattern is significant because it provides evidence for the wave nature of light. This phenomenon cannot be explained by classical particle theories of light, but is consistent with the wave theory of light proposed by scientists like Huygens and Young.

5. How can a single slit diffraction pattern be used in scientific research?

Single slit diffraction patterns have a wide range of applications in scientific research. They can be used to study the properties of light, such as its wavelength and polarization. They are also used in various imaging and measurement techniques, such as in microscopy and spectroscopy, to gather information about the structure and composition of materials.

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