A student conducts an experiment to determine the wavelength of monochromatic light from a laser. The student directs the laser beam normally at a diffraction grating. A screen is placed parallel to the grating at a variable distance xxx. The distance yyy from the central maximum to the first-order maximum on the screen is measured.
The diffraction grating has 800 lines mm−1800\text{ lines mm}^{-1}800 lines mm−1. The distance xxx is varied, and the distance yyy is measured for each position.
Show that the gradient of a graph of yyy against x2+y2\sqrt{x^2 + y^2}x2+y2 is equal to sinθ\sin \thetasinθ, where θ\thetaθ is the angle between the central maximum and the first-order maximum.
The student plots the experimental data on a graph of yyy against x2+y2\sqrt{x^2 + y^2}x2+y2. The straight line of best fit passes through the origin and the point (2.50 m,1.25 m)(2.50\text{ m}, 1.25\text{ m})(2.50 m,1.25 m).
Use these data to determine the wavelength λ\lambdaλ of the light from the laser.
Suggest why error bars are not shown on the graph if the absolute uncertainty in the distance measurements is very small (around ±1 mm\pm 1\text{ mm}±1 mm) compared to the overall scale of the axes.
Suggest how the precision of this experiment would be affected if the student used a standard protractor to measure the angle θ\thetaθ directly instead.
