Question

g Draw a diffraction pattern observed on a screen for the 1st order spectra for blue, green, orange and red lines from a given light source. This sketch should indicate the location of the 1st bright spot corresponding to blue, green, orange and red wavelengths.

Answer 1

θ₁ (blue) < θ₂ (green) < θ₃ (red)

Step-by-step 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