- Light of wavelength λ diffracts at a single rectangular slit of opening b. The diagram shows two rays of light leaving the top and middle of the slit. The rays come from the same wavefront. The angle of diffraction is θ. For small angles the approximation sin θ ≈ θ may be used.
The rays meet at point P on a screen a very large distance from the slit.
(a) (i) Show that the phase difference between the two rays at P is πbθ / λ. [2]
(ii) The two rays interfere destructively at P to form the first minimum of the single slit diffraction pattern. Explain why θ = λ/b. [1]
(b) The James Webb Space Telescope (JWST) has an effective diameter of 6.5 m.
(i) Calculate the smallest linear size at a distance of 13.6 billion light years (1.3 × 10²⁶ m) that can be resolved by the JWST when it operates at a wavelength of 1200 nm. [2]
(ii) The JWST can also operate at wavelengths longer than 1200 nm. Suggest whether the resolution of the telescope is improved at the longer wavelengths. [1]