Answer :
The wavelength of light being used is approximately 374 nm.
To find the wavelength of light being used in the grating with 3700 slits per cm and a third-order fringe at a 26.0° angle, we can use the grating equation:
nλ = d * sin(θ)
Where:
- n is the order of the fringe (n = 3 in this case)
- λ is the wavelength of light we want to find
- d is the distance between the slits (inverse of the number of slits per cm)
- θ is the angle of the fringe (26.0° in this case)
First, we need to find the distance between the slits (d). Since there are 3700 slits per cm, the distance between the slits is:
d = 1 / 3700 = 0.000270270 cm
Now, we can plug the values into the grating equation:
3λ = 0.000270270 cm * sin(26.0°)
To solve for λ, divide both sides by 3:
λ = (0.000270270 cm * sin(26.0°)) / 3
λ ≈ 3.74 × 10^(-7) cm
Convert the wavelength to nanometers (1 cm = 10^7 nm):
λ ≈ 374 nm
So, the wavelength of light being used is approximately 374 nm.
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