Finding the angular spread of a diffraction minima?

In summary, the question asks for the calculation of the angular spread of the first diffraction minima when light of wavelength 6000Å illuminates a single slit of width 10-4m. The relevant equations are d*y/D = nλ and Y = nλ/a for minima, where Y stands for the position on screen, d is slit width, and D is the separation between screen and slit. The angular spread of any maxima is the difference in the angles subtended by the two minima on either side of it, but the angular spread of a minima is not typically addressed due to the lack of a precise answer. Further clarification from the instructor may be needed.
  • #1
Peter Andrews
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1. Homework Statement
Light of wavelength 6000Å illuminates a single slit of width 10-4m. Calculate the angular spread of first diffraction minima.

Homework Equations


d*y/D = nλ
Y = nλ/a for minima
Y = (2n±1)λ/a for maxima
Y stands for the position on screen, d is slit width and D is separation between screen and slit.

The Attempt at a Solution


I understand that the angular spread of any maxima is the difference in the angles subtended by the two minima on either side of it. But what about angular spread of a minima? Is it the difference in the angles subtended by the two maxima on its either side?
 
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  • #2
Normally the width of the diffraction minima is a problem that is not addressed because there doesn't seem to be a precise answer to the question. Perhaps your instructor can provide further clarification.
 

1. What is diffraction and how does it relate to finding the angular spread of a diffraction minima?

Diffraction is the bending of waves around an obstacle or through an opening. In terms of finding the angular spread of a diffraction minima, it refers to the phenomenon where light waves are bent as they pass through a narrow slit, resulting in a pattern of dark and light fringes. The angular spread is a measure of the width of this diffraction pattern.

2. How is the angular spread of a diffraction minima calculated?

The angular spread of a diffraction minima can be calculated using the equation: θ = λ/d, where θ is the angular spread, λ is the wavelength of the light, and d is the width of the slit. This equation is based on the principles of diffraction and can be derived from the Huygens-Fresnel principle.

3. What factors can affect the angular spread of a diffraction minima?

The angular spread of a diffraction minima can be affected by several factors, including the wavelength of the light, the width of the slit, and the distance between the slit and the screen where the diffraction pattern is observed. Other factors such as the type of material the slit is made of and the level of coherence of the light source can also influence the angular spread.

4. How does the angular spread of a diffraction minima change as the width of the slit is varied?

As the width of the slit is varied, the angular spread of the diffraction minima also changes. A wider slit will result in a narrower diffraction pattern with a smaller angular spread, while a narrower slit will produce a wider diffraction pattern with a larger angular spread. This relationship is described by the equation θ = λ/d, where d is the width of the slit.

5. What practical applications does knowledge of the angular spread of a diffraction minima have?

Knowledge of the angular spread of a diffraction minima has many practical applications in fields such as optics, astronomy, and physics. It is used in the design and optimization of optical devices such as telescopes and microscopes, and in the analysis of diffraction patterns in materials. It is also important in understanding the behavior of light and other waves, and in studying the properties of particles such as electrons and atoms.

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