High School

A grating that has 3700 slits per cm produces a third-order fringe at a 26.0° angle.

Part A

What wavelength of light is being used? Express your answer to two significant figures and include the appropriate units.

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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