Answer:
θ₁ (blue) < θ₂ (green) < θ₃ (red)
Explanation:
A diffraction grating is a collection of equally spaced slits, thus fulfilling the relationship
d sin θ = m λ
where d is the distance between each pair of slits, λ the wavelength and m the order of diffraction
In this case, the first order is requested, so m = 1
let's find the angle for each wavelength
Blue, the wavelength is in the range of 450nm = 450 10⁻⁹m
θ₁ = sin-1 λ / d
θ₁ = sin-1 450 10⁻⁹ / d
Green, λ the order of 550 mn = 550 10-9 m
θ₂ = sin⁻¹ 550 10⁻⁹ / d
orange- red, wavelength 700 nm = 700 10⁻⁹ m
θ₃ = sin⁻¹ 700 10⁻⁹ / d
Note that d is the same since we are using the same diffraction grating, since the angles are small we can approximate the sine by its angle, therefore
θ₁ < θ₂ < θ₃
an outline of this spectrum can be seen in the attachment
