The Figure below shows the layout of a double-slit experiment, with two equal slits in an opaque screen, each of width b, separated by centre-to-centre distance a, where a > b. This is illuminated by parallel light from the left and produces a diffraction pattern on the second screen at distance s. a S Figure 1 The intensity pattern formed on the screen by the setup shown above is given by sin B (in) B I(0) = 410 a = sin 0, ka 2 2 where I, is the intensity at the centre of the pattern formed by one slit alone, and a, ß are defined by B cos² a, = kb 2 sin 0, and k = 2π/X. i) If the two slits have separation a = 0.8 mm, the slits are illuminated by a laser of wave- length = 633 nm, and the screen distance is s = 2 m, calculate the separation between adjacent dark fringes of the intensity pattern on the screen. ii) If the individual slits have a width b = 0.1 mm, draw an approximate sketch of the intensity pattern on the screen over the range -30 mm < y < +30 mm.

The Figure below shows the layout of a double-slit experiment, with two equal slits in an opaque screen, each of width b, separated by centre-to-centre distance a, where a > b. This is illuminated by parallel light from the left and produces a diffraction pattern on the second screen at distance s. a S Figure 1 The intensity pattern formed on the screen by the setup shown above is given by sin B (in) B I(0) = 410 a = sin 0, ka 2 2 where I, is the intensity at the centre of the pattern formed by one slit alone, and a, ß are defined by B cos² a, = kb 2 sin 0, and k = 2π/X. i) If the two slits have separation a = 0.8 mm, the slits are illuminated by a laser of wave- length = 633 nm, and the screen distance is s = 2 m, calculate the separation between adjacent dark fringes of the intensity pattern on the screen. ii) If the individual slits have a width b = 0.1 mm, draw an approximate sketch of the intensity pattern on the screen over the range -30 mm < y < +30 mm.