Determining the Wavelength of Laser Light Using Diffraction Grating
What is the wavelength of the laser light if light from a ruby laser strikes a diffraction grating with 6.00×10^5 slits per meter and the first order maximum is located 0.229 m from the central maximum?
The wavelength of the laser light is 1850 nm. The formula to determine the wavelength is wavelength = (order * slit spacing) / distance. Given that the first order maximum is located 0.229 m from the central maximum, the order is 1. The slit spacing is calculated by taking the inverse of the number of slits per meter (1/6.00×10^5 m). When we plug these values into the formula and simplify the equation, we get a wavelength of 1850 nm.
Calculation Method:
Number of slits per meter = 6.00×10^5 slits/m
Distance to screen = 0.500 m
Distance from central maximum to first order maximum = 0.229 m
Using the formula:
wavelength = (order * slit spacing) / distance
We have:
Order = 1
Slit spacing = 1 / 6.00×10^5 m
Distance = 0.229 m
By substituting the values into the formula:
wavelength = (1 * (1/6.00×10^5 m)) / 0.229 m
Simplifying the equation:
wavelength = (1 / 6.00×10^5) / 0.229
wavelength = 1.85×10^-6 m
To convert this to nanometers:
wavelength = 1.85×10^-6 m * 10^9 nm/m
wavelength = 1850 nm
Therefore, the wavelength of the laser light is 1850 nm.