Light of wavelength 620 nm from a laser is incident on a single rectangular slit of width 0.45 mm.

After passing through the slit, the light is incident on a screen that is a distance of 3.4 m from the slit. Calculate the distance between the centre and the first minimum of the diffraction pattern.

The laser in (a) is replaced by two identical lasers so that the light from both lasers illuminates the slit. The lasers are both 6.0 m from the slit. The two diffraction patterns on the screen are resolved according to the Rayleigh criterion.

(i) State what is meant by the Rayleigh criterion.

(ii) The minimum separation of the two laser beams is x. Determine x.

Compare the appearance of a single-slit diffraction pattern formed by laser light to that formed by a source of white light.

\(\theta  = \frac{{6.2 \times {{10}^{ - 7}}}}{{4.5 \times {{10}^{ - 4}}}}\left( { = 1.38 \times {{10}^{ - 3}}} \right)\);
distance ( =1.38×10^–3×3.4=4.68)≈4.7mm;

(i) in order to be (just) resolved the first minimum of diffraction pattern (of one image) coincides with the central maximum of the other (image) / OWTTE;

(ii) criterion specifies >4.7mm in this case / clear use of answer to (a) as distance;
\(\left( {\frac{{4.7}}{{3.4}} \times 6.0} \right) = 8.3{\rm{mm}}\);
Award [1 max] if factor of 1.22 used.

for white light:
central maximum white, laser central maximum is monochromatic;
white light fringes/lines will be coloured;
blue diffracted least / OWTTE;