Find Single slit diffraction width

In summary, the conversation discusses finding the slit width in a single-slit diffraction pattern using the equation a=m(lambda)D/y. The values provided in the problem are inconsistent with the values used in the equation, leading to a incorrect answer. The correct answer can be found by solving for a in the equation y_{5} - y_{1} = 0.400mm - resulting in a slit width of 0.001354mm.
  • #1
misunderstood
4
0
Ive been marked wrong but not sure why:

The distance between the first and fifth minima of a single-slit diffraction pattern is 0.400 mm with the screen 41.0 cm away from the slit, when light of wavelength 570 nm is used. Find the slit width.


y=m(theata)D/a

m-order = 5
D-distance from slit to screen = 0.43m
a-slit width = ?
y-distance from centre to minima = 0.000450 m

a=m(theata)D/y

((5)*(560x10^-9)*(0.43))/0.000450 = 2.6755x10^-3

The answer I got is 2.68x10^-3 but it's been marked wrong on the computer, is it me or is the answer correct??
 
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  • #2
I assume that by "theata" you actually mean the wavelength lambda.
I don't understand the values that you substitute into the equation; they don't match with the values you provided in the question at all.
 
  • #3
Im sorry the online test changes the values after you repeat the question

Ive changed it:
The distance between the first and fifth minima of a single-slit diffraction pattern is 0.450 mm with the screen 43.0 cm away from the slit, when light of wavelength 560 nm is used. Find the slit width.yes lambda as in wavelenght
 
  • #4
The value that you used is the distance of the 5th maxima from the origin (0th order maxima), and not the distance between the 1st and 5th maximas (or minimas - the distance is the same).
[tex]
y_{5} - y_{1} = 0.400mm
[/tex]

[tex]
\frac{5 \lambda D}{a} - \frac{1 \lambda D}{a} = 0.400mm
[/tex]
You can do the rest of the math.
 
  • #5
thankyou
 

Related to Find Single slit diffraction width

1. What is single slit diffraction and why is it important in science?

Single slit diffraction is a phenomenon in which light passing through a narrow slit is diffracted, or spread out, into a pattern of light and dark fringes. It is important in science because it allows us to study the behavior of light and understand the wave nature of light.

2. How is the width of a single slit diffraction pattern determined?

The width of a single slit diffraction pattern can be determined using the equation w = λL/d, where w is the width of the central maximum, λ is the wavelength of light, L is the distance between the slit and the screen, and d is the width of the slit. This equation is known as the single slit diffraction formula.

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

The width of a single slit diffraction pattern is affected by several factors, including the wavelength of light, the width of the slit, and the distance between the slit and the screen. The wider the slit, the narrower the central maximum will be. Similarly, the shorter the wavelength of light, the wider the central maximum will be. As the distance between the slit and the screen increases, the width of the central maximum decreases.

4. How does the single slit diffraction pattern change when the width of the slit is increased?

When the width of the slit is increased, the central maximum of the single slit diffraction pattern becomes wider and the intensity of the fringes decreases. This is because a wider slit allows more light to pass through, resulting in a broader diffraction pattern. Additionally, more interference occurs between the diffracted waves, causing the intensity to decrease.

5. What is the practical application of single slit diffraction?

Single slit diffraction has many practical applications, including in optical instruments such as microscopes and telescopes. It is also used in spectroscopy to analyze the wavelengths of light emitted by different sources. Additionally, single slit diffraction is used in the fabrication of diffraction gratings, which are used in many optical devices such as spectrometers and laser printers.

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