To find the wavelength of the unknown light in this interference pattern scenario, we can use the principles of Young's double slit experiment. The key information provided is that the central maximum of both light sources coincides, and the third bright fringe of the known light (590 nm) coincides with the fourth bright fringe of the unknown light. Let's break this down step by step.
Understanding Interference Patterns
In Young's double slit experiment, light waves passing through two closely spaced slits create an interference pattern on a screen. The positions of the bright fringes (maxima) are determined by the formula:
Where:
- y = position of the m-th bright fringe on the screen
- m = order of the fringe (0, 1, 2, ...)
- λ = wavelength of the light
- D = distance from the slits to the screen
- d = distance between the slits
Setting Up the Problem
Given that the third bright fringe of the known light (λ₁ = 590 nm) coincides with the fourth bright fringe of the unknown light (λ₂), we can express this mathematically. For the known light:
For the unknown light:
Since both fringes coincide, we can set y₁ equal to y₂:
Solving for the Unknown Wavelength
The distance D and the slit separation d cancel out from both sides, simplifying our equation to:
Now, we can solve for λ₂:
Substituting the known wavelength (λ₁ = 590 nm):
Calculating this gives:
Final Result
Thus, the wavelength of the unknown light is approximately 442.5 nm. This wavelength falls within the visible spectrum, specifically in the blue region of light. Understanding these relationships in interference patterns not only helps in solving this problem but also deepens our grasp of wave behavior in physics.
