To find the wavelength of the incident light in the Young's double-slit experiment, we can use the formula for the position of dark fringes. The position of the m-th dark fringe is given by the equation:
Understanding the Formula
The formula for the position of dark fringes is:
y_m = (m + 0.5) * (λ * L) / d
Where:
- y_m = position of the m-th dark fringe from the central maximum
- m = order of the dark fringe (0, 1, 2, ...)
- λ = wavelength of the light
- L = distance from the slits to the screen
- d = distance between the slits
Given Values
From the problem, we have:
- Distance between the slits, d = 0.25 cm = 0.0025 m
- Distance to the screen, L = 100 cm = 1 m
- Distance of the third dark fringe from the central bright fringe, y_3 = 0.059 cm = 0.00059 m
Calculating the Wavelength
We are looking for the third dark fringe, so m = 2 (since we start counting from zero). Plugging the values into the formula:
y_2 = (2 + 0.5) * (λ * L) / d
Substituting the known values:
0.00059 = 2.5 * (λ * 1) / 0.0025
Rearranging the Equation
Now, we can rearrange the equation to solve for λ:
λ = (0.00059 * 0.0025) / 2.5
λ = 0.00059 * 0.001
λ = 0.00000059 m = 590 nm
Final Answer
Thus, the wavelength of the incident light is 590 nm. Therefore, the correct option is c. 590 nm.
