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.
Which of the following equations describe the condition for observing the fourth dark fringe in an interference pattern correctly?
d sinè = ë
d sinè = 3ë/2
d sinè = 3ë
d sinè = 4ë
I was going to say d sinè = 4ë for dark fringe, but then i don't know what it is for bright fringe.
d sinθ = 4λ
To understand which equation describes the condition for observing the fourth bright fringe in Young's double-slit interference pattern, let's break down the concept of interference patterns.
In Young's double-slit experiment, a light wave passes through two narrow slits, creating two coherent sources of light. These two sources then interfere with each other, resulting in a pattern of alternating bright and dark fringes on a screen placed behind the slits.
For bright fringes, constructive interference occurs when the path difference between the two waves is an integer multiple of the wavelength (λ). Mathematically, this can be represented as:
d sinθ = mλ
Here, d represents the distance between the slits, θ is the angle between the incident light and the normal to the screen, m is the fringe number (where m = 0 represents the central bright fringe), and λ is the wavelength of the light.
To find the equation for the condition of the fourth bright fringe, we simply replace m with 4:
d sinθ = 4λ
Therefore, the equation describing the condition for observing the fourth bright fringe in Young's double-slit interference pattern is d sinθ = 4λ.
For dark fringes, destructive interference occurs when the path difference between the two waves is an odd multiple of half the wavelength (λ/2). Mathematically, this can be represented as:
d sinθ = (2m+1)(λ/2)
To find the equation for the condition of the fourth dark fringe, we replace m with 3 (as the fourth dark fringe has m = 3):
d sinθ = (2*3+1)(λ/2)
d sinθ = 3λ/2
Therefore, the correct equation describing the condition for observing the fourth dark fringe in an interference pattern is d sinθ = 3λ/2.
To summarize:
- Fourth bright fringe: d sinθ = 4λ
- Fourth dark fringe: d sinθ = 3λ/2