How Is Slit Width Calculated in Single Slit Diffraction?

In summary, the conversation discusses the calculation of slit width using a diffraction pattern produced by a single slit and monochromatic light. The distance from the center of the central maximum to the first-order maximum is given as 2.20 mm, and the values for wavelength, distance to the screen, and first-order maximum are provided. The equation y1 = L sin(theta) = L (wavelength / a) is used to solve for the slit width, resulting in a value of 0.0272 mm. The conversation ends with a request for clarification on any errors in the solution.
  • #1
SamTsui86
31
0

Homework Statement


A diffraction pattern is produced on a screen 130 cm from a single slit, using monochromatic light of wavelength 460 nm. The distance from the center of the central maximum to the first-order maximum is 2.20 mm. Calculate the slit width. (Hint: Assume that the first-order maximum is halfway between the first- and second-order minima.)


Homework Equations



y1 = L sin (theta) = L (wavelength / a)

The Attempt at a Solution



wavelength = 460 e -9 m
L = .13 m
y = .0022 m
so I found a

.0022 = .13 sin (theta)
sin (theta) = .0169 = (wavelength/ a)

a = .0272 mm

How anyone tell me what I am doing wrong?
 
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  • #2
[tex]130\;cm \neq 0.13\;m[/tex]

:wink:
 
  • #3
oops :) my bad
 

FAQ: How Is Slit Width Calculated in Single Slit Diffraction?

1. What is single slit diffraction?

Single slit diffraction is a phenomenon that occurs when a wave, such as light or sound, passes through a narrow opening or slit. The wave spreads out and creates a diffraction pattern, which is characterized by alternating bright and dark fringes.

2. How does single slit diffraction occur?

Single slit diffraction occurs because when a wave passes through a narrow opening, it bends or diffracts around the edges of the slit. This results in the wave spreading out and creating a pattern of constructive and destructive interference.

3. What factors affect the diffraction pattern in single slit diffraction?

The main factors that affect the diffraction pattern in single slit diffraction are the width of the slit, the wavelength of the wave, and the distance between the slit and the screen or detector. The wider the slit, the narrower the diffraction pattern will be. The shorter the wavelength, the wider the pattern will be. And the farther the screen or detector is from the slit, the more spread out the pattern will be.

4. What applications does single slit diffraction have?

Single slit diffraction has many applications in various fields, including physics, optics, and engineering. It is used to study the properties of waves and to determine the wavelength of a wave. It is also used in the design of optical instruments, such as telescopes and cameras, to improve their resolution.

5. How is single slit diffraction different from double slit diffraction?

Single slit diffraction occurs when a wave passes through a single narrow opening, while double slit diffraction occurs when a wave passes through two parallel narrow openings. The main difference between the two is that in single slit diffraction, the diffraction pattern consists of a single central maximum and alternating bright and dark fringes, while in double slit diffraction, the pattern consists of multiple central maxima and a more complex pattern of bright and dark fringes.

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