An experimenter shines monochromatic light through a single narrow slit and records…
PHYSICS · Single correct · A Level · Physics · Waves · Waves
Problem
An experimenter shines monochromatic light through a single narrow slit and records the distance from the central maximum to several dark fringes on a screen. The experimenter then uses all of these measured distances, rather than just the first‐order distance, to compute a single value of the wavelength. Which of the following best explains why this procedure generally produces a more precise value of the wavelength?
(a) Including more distant minima increases their angular separation, so the approximation sinθ≈θ becomes essentially exact, which yields a more precise wavelength.
(b) Because the formula mλ=asinθ multiplies the measured distance by the order number m, using several higher orders effectively magnifies the quantity being measured and reduces the percent uncertainty in the wavelength.
(c) Averaging the wavelengths calculated from several orders reduces the influence of random measurement uncertainties in locating each fringe.
(d) At higher orders the path difference is an integer multiple of the wavelength, allowing the experimenter to read the wavelength directly from the screen positions without dividing by m, so rounding errors are avoided.