A sodium-vapour lamp illuminates, with monochromatic yellow light, two narrow slits that are 1.00 mm apart. if the viewing screen is 1.00m from the slits and the distance from the central bright line to the next bright line is 0.589 mm, what is the wavelength of the light?
can someone please explain the question to me??
Refer to the double-slit diffraction experiment. There are actually two wavelengths in a sodium lamp, but they are close together and the average wavelength is 589.3 nm. That should be your answer.
Uses the equation that relates the separation of the central bright line and the first fringe to (wavelength)/(slit separation) ratio times the viewing screen distance.
For more about the physics, read this:
http://www.studyphysics.ca/newnotes/20/unit04_light/chp1719_light/lesson58.htm
Sure! The question is asking for the wavelength of the monochromatic yellow light that is being passed through two narrow slits in a sodium-vapour lamp.
The problem provides the following information:
- The distance between the two slits is 1.00 mm.
- The distance from the slits to the viewing screen is 1.00 m.
- The distance from the central bright line to the next bright line on the viewing screen is 0.589 mm.
To solve this problem, we can use the concept of interference in waves. When light passes through two slits, it creates an interference pattern on the screen due to the overlapping of the waves. This pattern consists of alternating bright and dark fringes.
The key is to recognize that the distance between adjacent bright lines (also known as fringes) is related to the wavelength of the light and the geometry of the setup. In this case, we are given the distance between two adjacent fringes, which is 0.589 mm.
The formula that relates the fringe separation distance (d), the wavelength (λ), and the distance from the slits to the viewing screen (L) is given by:
λ = d * L / y
Where:
- λ is the wavelength of the light
- d is the fringe separation distance (0.589 mm)
- L is the distance from the slits to the screen (1.00 m)
- y is the distance between the central bright line and the desired fringe line (this will be equal to half the fringe separation distance in this case)
In this problem, the desired fringe line is one step away from the central bright line, so y = 0.589 mm / 2 = 0.2945 mm.
By substituting the known values into the formula, we can calculate the wavelength:
λ = 0.589 mm * 1.00 m / 0.2945 mm
Converting the units to match, we get:
λ = 0.589 mm * (1.00 m / 1000 mm) / 0.2945 mm
Simplifying the calculation, we get:
λ ≈ 1.999 m
Therefore, the wavelength of the monochromatic yellow light is approximately 1.999 meters.