Outline what is meant by the term

(i)     coherent.

(ii)     monochromatic.

State the phase difference between the light waves from the two slits that meet at B.

(i)     Show that the laser produces light of wavelength equal to 720 nm.

(ii)     State the path difference, in metres, between the waves that meet at B.

Determine the number of lines per metre of the diffraction grating.

(i)     constant/zero phase difference (between the light waves);

(ii)     single/same wavelength/frequency; (allow “narrow band” OWTTE)

Do not allow “single colour”.

\(180^\circ /\pi {\text{rad}}\);

Do not accept \(\frac{\lambda }{2}\).

(i)     use of \(\lambda  = \frac{{sd}}{D}\);

\(s = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{2}  \times 1.8{\text{ (mm)}}\); (award this mark for any evidence for the factor of 2)

\(\lambda  = \frac{{{\text{2}} \times {\text{1.8}} \times {\text{1}}{{\text{0}}^{ - 3}} \times {\text{0.30}} \times {\text{1}}{{\text{0}}^{ - 3}}}}{{{\text{1.5}}}}\) / OWTTE;

\({\text{(}} = 7.2 \times {10^{ - 7}}{\text{ m)}}\)

Exact answer is given, award marks for correct working.

(ii)     \({\text{3.6}} \times {\text{1}}{{\text{0}}^{ - 7}}{\text{ m}}\)\(\,\,\,\)or\(\,\,\,\)360 nm;

Allow ECF from (c)(i).

use of \(d = \frac{{n\lambda }}{{\sin \theta }}\);

\(d = \frac{{3 \times 720 \times {{10}^{ - 9}}}}{{\sin 39^\circ }} = 3.4 \times {10^{ - 6}}{\text{ (m)}}\);

\(N = \left( {\frac{1}{{3.4 \times {{10}^{ - 6}}}} = } \right){\text{ }}2.9 \times {10^5}\);

Award [3] for a bald correct answer.

ECF examples:

Award [2 max] if n = 2 is used (gives 4.4 \( \times \) 10⁵).

Award [2 max] if 78° is used (gives 4.5 \( \times \) 10⁵).

Award [2 max] if 13° and n = 1 used (gives 3.1 \( \times \) 10⁵).