Explain how to determine the wavelength of light using a laser and a diffraction grating, including a labeled diagram.

Here's how to determine the wavelength of light using a laser and a diffraction grating: Diagram (2 marks) [ thick, laser/.pic= (0,0) rectangle (1,0.5); [fill=red] (0.8,0.25) circle (0.1); [red,->] (1,0.25) -- (2,0.25); at (0.5,0.7) Laser; , grating/.pic= (0,0) -- (0,1); in 0.1,0.2,...,0.9 (0,) -- (0.2,); at (0.1,1.2) Grating; , screen/.pic= (0,0) rectangle (0.2,3); at (0.1,3.2) Screen; ] % Laser at (0,1.5) laser; % Diffraction Grating at (3,1.5) grating; % Screen at (8,0) screen; % Laser beam path [red,->] (2,1.75) -- (3,1.75); % From laser to grating % Diffracted beams [red,->] (3.2,1.75) -- (8,1.75); % Central maximum (n=0) [red,->] (3.2,1.75) -- (8,2.5); % First order (n=1) [red,->] (3.2,1.75) -- (8,1.0); % First order (n=1) % Labels for maxima at (8.5,1.75) n=0; at (8.5,2.5) n=1; at (8.5,1.0) n=1; % Distances [<->] (3.1,0.5) -- (8.1,0.5); at (5.6,0.7) L; % Distance from grating to screen [<->] (8.3,1.75) -- (8.3,2.5); at (8.6,2.125) x; % Distance from central to first order % Angle (3.2,1.75) -- (8,1.75); (3.2,1.75) -- (8,2.5); [draw, angle radius=1cm, ""] angle = 8-1.75-3.2 -- 8-1.75-8 -- 8-2.5-8; Observation (2 marks) When the laser beam passes through the diffraction grating, a pattern of bright spots (maxima) is observed on the screen. There is a very bright central spot (the central maximum, n=0). Symmetrically on either side of the central maximum, there are other bright spots (first-order maxima, n=1; second-order maxima, n=2, etc.). The intensity of the bright spots decreases as the order (n) increases, moving away from the central maximum. Calculations (4 marks) 1. Determine grating spacing (d): The diffraction grating is usually labeled with the number of lines per millimeter (e.g., 300 lines/mm). Convert this to lines per meter, then find the spacing d between adjacent lines: d = (1)/(number of lines per meter) For example, if it's 300 lines/mm: d = (1)/(300 lines/mm) = (1)/(300 × 1000 lines/m) = (1)/(3 × 10^5 lines/m) d = 3.33 × 10^-6 m 2. Measure distances: Measure the distance L from the diffraction grating to the screen. Measure the distance 2x between the two first-order maxima (the bright spots on either side of the central maximum). Then, x = (2x)/(2). 3. Calculate the angle of diffraction (): Use trigonometry: = (x)/(L) Then, calculate = ((x)/(L)). For small angles, ≈ . 4. Calculate the wavelength (): Use the diffraction grating formula: d = n For the first-order maximum, n=1. Rearrange to find : = (d )/(n) Substitute the values of d, , and n=1 to obtain the wavelength of the laser light. Precaution (2 marks) Laser Safety: Never look directly into the laser beam* as it can cause permanent eye damage. Ensure the beam is directed away from people's eyes. Dark Room: Conduct the experiment in a darkened room* to clearly observe the diffraction pattern and accurately measure the positions of the maxima. Perpendicular Alignment: Ensure the laser beam is perpendicular* to the diffraction grating to avoid errors in the angle measurement. Accurate Measurements: Take multiple readings* for x and L and calculate their averages to minimize random errors. That's 2 down. 3 left today — send the next one.