A red laser of wavelength λ=650nm passes through a single narrow slit of unknown width. A photodetector mounted on a rotating arm measures how the light intensity varies with the angle θ relative to the central axis. The first points at which the detected intensity falls to essentially zero occur at θ=±3.0∘. Assume the angles involved are small enough that the approximation sinθ≈θ (with θ in radians) is acceptable for estimating numerical values.
(a) Determine the width of the slit in micrometres, showing all reasoning steps and keeping at least two significant figures in intermediate calculations.
(b) Estimate the full angular width of the central maximum (from the first minimum on one side to the first minimum on the other) in degrees.
(c) A student claims that the small–angle approximation produces an error of less than 1% in the calculated slit width for this experiment. Show quantitatively whether the student’s claim is valid.