Calculating Slit Width for Diffraction Pattern

[Jacob87411]

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?

 

[Jacob87411]

Does this look right or did i go wrong somewhere? Any help is appreciated greatly

 

[thepatientmental]

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.