Calculating Slit Width for Diffraction Pattern

In summary, a diffraction pattern is produced on a screen 140 cm from a single slit using monochromatic light of wavelength 500 nm. The distance from the center of the central maximum to the first order maximum is 3 mm. To calculate the slit width, the equation sin angle = (M * wavelength) / d is used, where M is the order of the maximum and d is the distance between the slit and the screen. In this case, the first order maximum is halfway between the first and second order minima.
  • #1
Jacob87411
171
1
A diffraction pattern is produced on a screen 140 cm from a single slit using monochromatic light of wavelength 500 nm. The distance from the center of the central maximum to the first order maximum is 3 mm. Calculate the slit width (assume first order maximum is halfway between the first and second order minima).

So things we know-
From the slit to the screen is 140 cm
Wavelength = 500 nm
from the center of the central maximum to the first order is 3 mm.

if we use: Sin of the angle = (M * Wavelength)/d =
sin of the angle = (1 * 500x10^-7) / .003

That gives the angle of the central maximum which we can then plug into
sin angle=wavelength/slit width?
 
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  • #2
Does this look right or did i go wrong somewhere? Any help is appreciated greatly
 
  • #3


To calculate the slit width, we can use the formula d = (m * λ)/sinθ, where d is the slit width, m is the order number, λ is the wavelength, and θ is the angle from the central maximum to the first order maximum. In this case, we are given the values of m = 1, λ = 500 nm, and θ = 3 mm/140 cm = 0.0214 rad. Plugging these values into the formula, we get:

d = (1 * 500x10^-9)/sin(0.0214)
= (500x10^-9)/0.0214
= 0.0233 mm

Therefore, the slit width is approximately 0.0233 mm. This means that the slit should be very narrow in order to produce a diffraction pattern with distinct and well-separated maxima and minima.
 

Related to Calculating Slit Width for Diffraction Pattern

1. How do I calculate the slit width for a diffraction pattern?

To calculate the slit width for a diffraction pattern, you can use the equation: w = λL/D, where w is the slit width, λ is the wavelength of light, L is the distance from the slit to the screen, and D is the distance between the slits.

2. What is the significance of calculating the slit width for a diffraction pattern?

Calculating the slit width for a diffraction pattern allows us to understand and predict the pattern of light that will be diffracted by a given slit. This is important in fields such as optics and astronomy, where diffraction patterns can provide valuable information about the properties of light sources.

3. What factors can affect the accuracy of calculated slit width for a diffraction pattern?

The accuracy of the calculated slit width for a diffraction pattern can be affected by various factors such as the quality of the light source, the precision of the measuring instruments, and any obstructions or imperfections in the slit itself. Additionally, environmental factors such as temperature and air density can also impact the accuracy of the calculation.

4. Can the equation for calculating slit width be applied to all types of waves?

Yes, the equation w = λL/D can be applied to all types of waves, as long as the wavelength of the wave is known. This includes not only light waves, but also sound waves, water waves, and other types of waves.

5. Is there a maximum or minimum slit width that can be calculated for a diffraction pattern?

Theoretically, there is no maximum or minimum slit width that can be calculated for a diffraction pattern. However, in practical applications, the slit width should be small enough to produce a visible diffraction pattern, but not so small that it becomes difficult to measure accurately. Additionally, the slit width should also be larger than the wavelength of the light being used to ensure a clear diffraction pattern.

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