Answer:
3 order dark fringe
Explanation:
y = Distance from central bright fringe = 204 mm
λ = Wavelength = 400 nm
L = Distance between screen and source = 1 m
d = Slit distance = 6 μm
[tex]tan\theta =\frac{y}{L}\\\Rightarrow tan\theta =\frac{204}{1000}=0.2012^{\circ}[/tex]
[tex]dsin\theta=m\lambda\\\Rightarrow m=\frac{dsin\theta}{\lambda}\\\Rightarrow m=\frac{6\times 10^{-6}sin0.2012}{400\times 10^{-9}}=2.9982\approx 3[/tex]
Order of fringe is 3
So, it is a Dark order fringe
This question involves the concept of Young's Double Slit Experiment formula, diffraction grating, and fringe spacing.
The fringe located at a linear distance y = 204 mm to the left of the central bright fringe is "3rd order Dark Fringe".
Young's double-slit formula can be written as follows for the diffraction grating:
[tex]y = \frac{m\lambda L}{d}\\\\m = \frac{yd}{\lambda L}[/tex]
where,
m = order of diffraction = ?
y = fringe spacing = 204 mm = 0.204 m
d = slit separation = 6 μm = 6 x 10⁻⁶ m
L = screen distance = 1 m
λ = wavelength = 400 nm = 4 x 10⁻⁷ m
Therefore,
[tex]m = \frac{(6\ x\ 10^{-6}\ m)(0.204\ m)}{(4\ x\ 10^{-7}\ m)(1\ m)}[/tex]
m = 3
Due to the odd-order number, it will be a dark fringe.
Learn more about Young's Double Slit Experiment here:
brainly.com/question/13935986?referrer=searchResults
The attached picture shows Young's Double Slit Experiment.
