When light of wavelength 450 nm is passed through a certain diffraction

grating, the first order diffraction maximum is found to be at an angle of 35° to the
straight through. Calculate the distance between adjacent slits in the grating.

To calculate the distance between adjacent slits in the grating, we can use the formula for the angular position of the diffraction maximum:

dsinθ = mλ

Where:
d = distance between adjacent slits
θ = angle of diffraction
m = order of diffraction (in this case, m = 1 since it is the first order)
λ = wavelength of light

Given:
θ = 35°
λ = 450 nm = 450 x 10^-9 m
m = 1

Now we can solve for d:

d = (mλ) / sinθ

d = (1)(450 x 10^-9 m) / sin(35°)

Using a calculator, compute sin(35°) ≈ 0.574

d ≈ (1)(450 x 10^-9 m) / 0.574

d ≈ 7.84 x 10^-7 m

Therefore, the distance between adjacent slits in the grating is approximately 7.84 x 10^-7 meters.

To calculate the distance between adjacent slits in the grating, we can use the equation for the path difference in a diffraction grating.

The path difference (Δx) is given by the equation:

Δx = d * sin(θ)

Where:
Δx is the path difference
d is the distance between adjacent slits
θ is the angle of diffraction

In this case, we know the wavelength (λ) of light is 450 nm (or 450 x 10^(-9) meters) and the angle of diffraction (θ) is 35°.

First, we need to convert the angle from degrees to radians:

θ_rad = θ * (π/180)
θ_rad = 35 * (π/180) ≈ 0.6109 radians

Next, we can rearrange the equation to solve for d:

d = Δx / sin(θ)

Since this is the first-order diffraction maximum, the path difference (Δx) is equal to the wavelength (λ).

d = λ / sin(θ_rad)
d = (450 x 10^(-9) m) / sin(0.6109)
d ≈ 7.153 x 10^(-7) m

Therefore, the distance between adjacent slits in the grating is approximately 7.153 x 10^(-7) meters, or 0.7153 μm.