Single-slit diffraction and small angle approximation

In summary, the distance from the slit to the screen should be 0.0109 m to have the first minimum at 0.85 mm from the central maximum, and the width of the central maximum is calculated to be 0.0103 mm using the small angle approximation.
  • #1
konto77
13
0

Homework Statement



Light of wavelength 587.5 nm illuminates a single 0.75 mm wide slit. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85 mm from the central maximum? (b) Calculate the width of the central maximum.
Use the small angle approximation.

lambda = 587.5 nm
y=0.85 mm
a=0.75 mm

Homework Equations



y=L*lambda/a

The Attempt at a Solution



I easily found part a to be L = 0.0109 m. But i am having trouble finding out part b.

I tried 2*0.0109 m = .0218 but i don't know if that's right since i don't have the answer.




Any help is appreciated.
 
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  • #2
The central maximum of the diffraction pattern from the slit subtends an angle ##\Delta \theta =\dfrac{\lambda}{d}## where ##d## is the slit width. In the small angle approximation, the width of the maximum on the screen is ##w=L~\Delta \theta=\dfrac{\lambda~L}{d}.##
 

FAQ: Single-slit diffraction and small angle approximation

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. This causes the wave to spread out and create a pattern of interference and diffraction on the other side of the slit.

2. How does the size of the slit affect single-slit diffraction?

The size of the slit directly affects the diffraction pattern. A wider slit will produce a narrower diffraction pattern, while a smaller slit will produce a wider pattern.

3. What is the small angle approximation in single-slit diffraction?

The small angle approximation is a mathematical simplification used to calculate the diffraction pattern when the slit width is much smaller than the wavelength of the wave. This allows for easier calculations and more accurate results.

4. Can single-slit diffraction be observed with the naked eye?

Yes, single-slit diffraction can be observed with the naked eye. It is commonly seen in everyday situations, such as when light passes through a small opening in a window blind or when sound passes through a narrow doorway.

5. How is single-slit diffraction used in scientific research?

Single-slit diffraction is commonly used in scientific research to study the properties of waves, such as light and sound. It is also used in areas such as X-ray crystallography to analyze the structure of crystals by measuring the diffraction pattern produced by X-rays passing through a crystal lattice.

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