Which of the following equations describe the condition for observing the fourth dark fringe in an interference pattern correctly?
d sinθ = λ
d sinθ = 4λ
d sinθ = 5λ/2
d sinθ = 7λ/2
I would think B but I feel like the answer that has a '4' in it (fourth fringe, four... yeah) would be too obvious
d•sinθ=2k•λ/2=k λ
k=4
d•sinθ==4 λ
To determine the correct equation for observing the fourth dark fringe in an interference pattern, we need to understand the concept of interference and how fringes are formed.
In interference patterns, light waves from two coherent sources (such as two slits or reflections) overlap and interfere with each other. This interference results in alternate bright and dark fringes on a screen or observation plane.
The condition for observing the fringes is given by the equation:
d sinθ = mλ
where:
- d is the distance between the sources or slits
- θ is the angle at which the fringe is observed
- m is the order of the fringe (1, 2, 3, ...)
- λ is the wavelength of light
In this case, we are interested in the fourth dark fringe, which means m = 4 (since dark fringes are always even orders). Plugging in m = 4, we get:
d sinθ = 4λ
So, the correct equation for observing the fourth dark fringe in an interference pattern is:
d sinθ = 4λ
Therefore, option B, "d sinθ = 4λ," is indeed the correct choice. The presence of the number 4 in the equation indicating the fourth fringe is not just a coincidence but a reflection of the order of the fringe.