Finding the width of a diffraction slit

The problem is asking for the width of a slit that will produce a particular diffraction pattern, for different types of electromagnetic waves. The diffraction pattern is a function of the wavelength and the width of the slit.In summary, the problem is asking for the width of a diffraction slit that is seven times larger than the wavelength for different electromagnetic waves, including a radio wave, cell phone signals, red light, and X-rays. The relationship between frequency and wavelength is given by \lambda=\frac{c}{f}.
  • #1
theskyisgreen
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Homework Statement


Single-slit diffraction can be observed with any type of electromagnetic wave (not just light). Suppose you want to make a diffraction slit whose width is seven times larger than the wavelength for the following cases. How wide would the slit be?

(a) A radio wave for your favorite FM station (f = 100 MHz)


(b) The waves that carry your cell phone signals (f = 2.0 GHz)


(c) Red light (f = 5e14 Hz)


(d) The X-rays used in your dentist's office (f ≈ 4e20Hz)



Homework Equations





The Attempt at a Solution


I honestly have no idea where to begin with this.
I do know that the answer to a) is 7*3.. but I don't know why?
If anyone can point me in the right direction it would be appreciated.
 
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  • #2
The relationship between frequency and wavelength is

[tex]\lambda=\frac{c}{f}[/tex]

where c is the speed of light. The problem has nothing to do with diffraction.
 

Related to Finding the width of a diffraction slit

1. What is diffraction?

Diffraction is a phenomenon in which waves, such as light or sound, spread out and bend around obstacles. It occurs when the wavelength of the wave is similar to the size of the obstacle it encounters.

2. How is diffraction related to finding the width of a slit?

The width of a diffraction slit is directly related to the amount of diffraction that occurs. The narrower the slit, the more diffraction will occur, resulting in a wider diffraction pattern.

3. Why is finding the width of a diffraction slit important?

Knowing the width of a diffraction slit is important because it helps us understand the properties of light and other waves. It also has practical applications in fields such as optics and astronomy, where precise measurements of light patterns are necessary.

4. How can the width of a diffraction slit be determined?

The width of a diffraction slit can be determined by measuring the distance between the central maximum and the first minimum of the diffraction pattern. This distance is related to the wavelength of the wave and the width of the slit through a mathematical formula known as the diffraction equation.

5. What factors can affect the measurement of the width of a diffraction slit?

The width of a diffraction slit can be affected by factors such as the wavelength and intensity of the wave, the distance between the slit and the screen, and any imperfections or irregularities in the slit itself. Other external factors, such as ambient light or vibrations, can also impact the accuracy of the measurement.

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