Which of the following equations describes the condition for observing the fourth bright fringe in Young's double-slit interference pattern? Assume n = 0 for the central bright fringe.
d sinθ = λ
d sinθ = 3λ/2
d sinθ = 3λ
d sinθ = 4λ
d•sinθ=2k•λ/2=k λ
k=4
d sinθ = 4λ
To determine the equation that describes the condition for observing the fourth bright fringe in Young's double-slit interference pattern, we can use the formula:
y = mλL / d
Where:
y is the position of the fringe (distance from the central maximum),
m is the fringe order (0 for the central maximum, 1, 2, 3, ... for the bright fringes),
λ is the wavelength of light,
L is the distance from the double-slit to the screen (also known as the "screen-slit distance"), and
d is the distance between the two slits in the double-slit experiment.
For the fourth bright fringe, m = 4. So the equation becomes:
y = (4λL) / d
Now, since we want to determine the condition for observing the fourth bright fringe, we need to express this equation in terms of θ (theta) instead of y. We can use the small angle approximation, which states that sinθ ≈ θ for small angles.
Rearranging the equation above, we get:
y = (4λL) / d
4λL / d = sinθ
Now, we can rewrite the equation in terms of sinθ:
d sinθ = 4λL
Therefore, the equation that describes the condition for observing the fourth bright fringe in Young's double-slit interference pattern is:
d sinθ = 4λ.
So, the correct equation from the options given is:
d sinθ = 4λ.