Question

Aim Diffraction grating is used to determine the wavelengths of light emitted by various sources, ranging from excited gases to LED's to stars. In this project, your task is to propose how the data from an imagined diffraction-grating experiment must be analysed to determine an unknown wavelength. Introduction A diffraction grating contains many parallel slits, where the distance d between adjacent slits is very small. If we shine light of a particular wavelength on a diffraction grating, an interference pattern is formed on the screen behind the grating. If the distance L from the grating to the screen is much greater than d, the pattern consists of well-separated narrow bright fringes or lines, which are each labelled by an integer m (= 0 or 1 or 2 or ...) called the order number. The m=0 line is at the centre of the screen, followed by the m=1 lines symmetrically on both sides of the m=0 line, and so on (Figure 1). Intensity of fringe m = 2 grating m = 0 m = 1 m = 2

(1) Derive the equation that relates the wavelength λ to the distance Ym=1 of the m=1 line.

You must provide the justification for your derivation.

(2) Describe, step by step, how the experimental data has to be analysed to determine the

unknown wavelength λ3. You must be brief but clear in your description of the method.

**You can just show me the working, I will provide explanations on my own**