State the Rayleigh criterion.

(i)     Calculate the angular separation of the two towers when the images of the towers are just resolved by Emlyn.

(ii)     Emlyn can just resolve the images of the two towers when his distance from the towers is 11 km. Determine the distance between the two towers.

Emlyn puts on a pair of polarizing sunglasses. Explain how these sunglasses reduce the intensity of the light, reflected from the sea, that enters Emlyn’s eyes.

for the images (of two sources) just to be resolved/distinguished/seen as separate;

central maximum of one diffraction pattern must coincide with first minimum of second / OWTTE;

Accept a suitably drawn diagram for the second marking point.

(i)     \(\theta  = \left( {\frac{{{\text{1.22}} \times {\text{550}} \times {\text{1}}{{\text{0}}^{ - 9}}}}{{{\text{2.0}} \times {\text{1}}{{\text{0}}^{ - 3}}}} = } \right){\text{ }}3.4 \times {10^{ - 4}}{\text{ (rad)}}\)\(\,\,\,\)or\(\,\,\,\)0.019°;

(ii)     \(d = 11 \times {10^3} \times 3.4 \times {10^{ - 4}}\);

\( = {\text{3.7 (m)}}\);

Award [2] for a bald correct answer.

reflected light is (partially) polarized parallel to sea surface/horizontally polarized;

sunglasses have a transmission axis at 90° to reflected light/vertical transmission axis;

An improvement in the answers to (a) was noted.

In (b) very few omitted to use the factor of 1.22 and full marks were often scored for both calculations.

(d) was poorly answered with many being unable to make it clear that reflected light from the sea would be partially horizontally polarized. Some just referred to the darkness of the sunglasses' lens.