Two parallel slits are illuminated by light of two wavelengths one of which is 5.8*10exp -7m .On the screen the fourth dark line of known wavelength coincides with the fifth bright line of light unknown wavelength.Find the unknown wavelength?
To find the unknown wavelength, let's break down the problem and analyze the given information:
1. We have two parallel slits illuminated by light of two different wavelengths.
2. One of the known wavelengths is given as 5.8 × 10^(-7) m.
3. On the screen, the fourth dark line of the known wavelength coincides with the fifth bright line of the unknown wavelength.
In this case, we can use Young's double-slit experiment and the interference equation to solve the problem. The interference equation is given by:
λ = (m x d x λ_unknown) / D
Where:
- λ is the wavelength of the unknown light.
- m is the order of the bright or dark fringe.
- d is the distance between the slits (which is unknown in this case).
- D is the distance between the slits and the screen.
We are given that the fourth dark line of the known wavelength coincides with the fifth bright line of the unknown wavelength. Let's assume the order of the bright line is m1 = 5 and the order of the dark line is m2 = 4.
We can set up two equations based on the given information:
Equation 1: λ_known = (m1 x d x λ_unknown) / D
Equation 2: λ_known = (m2 x d x λ_unknown) / D
Since both equations have the same value for λ_known, we can equate them:
(m1 x d x λ_unknown) / D = (m2 x d x λ_unknown) / D
Canceling out the common factors:
m1 x d = m2 x d
Since m1 = 5 and m2 = 4, we can solve for the unknown wavelength:
5 x d = 4 x d
d cancels on both sides, yielding:
5 = 4
This equation is not possible, which suggests that there might be an error in the given information or in the calculations. Please double-check the data or provide any additional information to help us resolve the issue.