A Michelson interferometer is set up to give circular fringes and illuminated with light in the spectral range 800-900 nm by a caesium light source. The intensity I(2) at the centre of the interference pattern is recorded as a function of the distance x of the moving mirror from that corresponding to zero path difference. It is found to have the form [(x) = 10 [3 + 3 cos(K12) cos(K2x) - sin(K12) sin(K2x)] , where K1 =1.44 x 107m⁻¹, K2 = 3.48 x 10 m⁻¹ and I, is a constant. Make a sketch of the interference pattern over the range -10 < x < 10 pm. When the interference pattern is recorded over a much larger range of path difference, it is found that the periodic terms in the pattern are in fact multiplied by a function f(x) « exp(-K3.22). Suggest what might cause this effect (hint: use your knowledge of the convolution theorem).