What is the slit spacing of a diffraction necessary for a 600 nm light to have a first order principal maximum at 25.0°?

To find the slit spacing (d), also referred to as 'grating spacing,' for a diffraction grating that results in a first-order principal maximum at a specific angle, you can use the diffraction grating equation for constructive interference, which is given by:

nλ = d sin(θ)

Where: - n is the order number of the principal maximum (n=1 for first-order principal maximum) - λ is the wavelength of the light (in meters) - d is the slit spacing (also known as grating constant or line spacing) - θ is the diffraction angle where the principal maximum occurs.

Rearranging this equation to solve for d gives:

d = nλ / sin(θ)

Given that λ = 600 nm (1 nm = 10^-9 meters), n = 1 for the first order maximum, and θ = 25.0°, you can plug in the values:

d = (1 * 600 * 10^-9 m) / sin(25.0°)

First, calculate the sine of 25.0°:

sin(25.0°) ≈ 0.4226

Now substitute this value into the equation to solve for d:

d ≈ (1 * 600 * 10^-9 m) / 0.4226 d ≈ (600 * 10^-9 m) / 0.4226

d ≈ 1.419 * 10^-6 m

d ≈ 1420 * 10^-9 m

Expressed in nanometers:

d ≈ 1420 nm