Question 18M.2.HL.TZ1.3

superposition of light from each slit / interference of light from both slits

with path/phase difference of any half-odd multiple of wavelength/any odd multiple of $\pi$ (in words or symbols)

producing destructive interference

Ignore any reference to crests and troughs.

[3 marks]

light waves (from slits) must have constant phase difference / no phase difference / be in phase

OWTTE

[1 mark]

evidence of solving for D «D $=\frac{sd}{\lambda }$» ✔

«$\frac{4.50\times {10}^{-3}\times 0.300\times {10}^{-3}}{633.0\times {10}^{-9}}\times 2$» = 4.27 «m» ✔

Award [1] max for 2.13 m.

sin θ = $\frac{4\times 633.0\times {10}^{-9}}{0.300\times {10}^{-3}}$

sin θ = 0.0084401…

final answer to three sig figs (eg 0.00844 or 8.44 × 10^–3)

Allow ECF from (a)(iii).

Award [1] for 0.121 rad (can award MP3 in addition for proper sig fig)

Accept calculation in degrees leading to 0.481 degrees.

Award MP3 for any answer expressed to 3sf.

[3 marks]

use of diffraction formula «b = $\frac{\lambda }{\theta }$»

OR

$\frac{633.0\times {10}^{-9}}{0.00844}$

«=» 7.5«00» × 10^–2 «mm»

Allow ECF from (b)(i).

[2 marks]

wavelength increases (so frequency decreases) / light is redshifted

galaxy is moving away from Earth

Allow ECF for MP2 (ie wavelength decreases so moving towards).

[2 marks]