Problem 5: Finding Angle for Third Order Maximum of Yellow Light

What is the angle for the third-order maximum for yellow light with a wavelength of 565 nm falling on a diffraction grating with 1500 lines per centimeter?

The angle for the third-order maximum for the yellow light is approximately 1.44 degrees. To find this angle, we can use the grating equation, which relates the order of the maximum, the wavelength of the light, the grating spacing, and the angle of diffraction.

Grating Equation and Calculation

Given: λ = 565 x 10⁻⁹ m, d = 1 / (1500 lines/cm) = 6.67 x 10⁻⁶ m, n = 3.
The grating equation states: n * λ = d * sin(θ), where n is the order of the maximum, λ is the wavelength of the light, d is the grating spacing, and θ is the angle of diffraction.
Substitute the given values into the equation: 3 * 565 x 10⁻⁹ m = 6.67 x 10⁻⁶ m * sin(θ).
Solving for θ: θ = sin⁽⁻¹⁾((3 * 565 x 10⁻⁹m) / (6.67 x 10⁻⁶ m)) = 0.0252 rad.
Convert the angle to degrees: θ = 0.0252 rad * (180° / π rad) = 1.44°.

Principle of Diffraction

When light passes through a diffraction grating, it diffracts into multiple orders of maxima due to constructive interference. The grating equation helps in determining the angles at which these maxima occur based on the wavelength of light and the characteristics of the grating.
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