A question concerning interference and diffraction 
hi, I have recently been doing this problem and when looking at the mark scheme for d iii it says the secondary maxima intensity decreases however I believe this not to be true. Understanding it to be in reference to the reflected wave from the plate which is at zero displacement moving at maximum velocity back towards the source. the interference is the 'single slit' interference with itself as all waves do, so we know that the reflected wave has a shorter wavelength as its reflected and can be treated as a moving source. so the angle of the centre of the primary maxima is unchanged of course as it is zero, the width decreases as theta  = lambda / aperture so wavelength is proportional to angle and the width decreases with a smaller wavelength. But d)iii) claims that the intensity of the secondary maxima will decrease, which doesn't make any sense to me. Could someone please give me some help on why my thinking is wrong and explain how I can go about understanding this.
 A: I interpret the question in such a way that (d.i), (d.ii), and (d.iii) are referencing the image at the top:

If this is the case, the question asking us to interpret some properties of of the principal and secondary maxima if there are five slits instead of four.
A convenient way to represent this problem is using equations for diffraction gratings, where the intensity of the resulting maxima depend on the number of slits $(N)$. Principal maxima depend on $N^2$, and secondary maxima depend on $\frac{N^2}{1+(N^2-1)\sin^2(\beta)}$. The ratio (secondary/principal) of these dependencies then shows us how the secondary maxima hold up against the principal maxima for varying $N$: $$\frac{I_S}{I_P}=\frac{1}{1+(N^2-1)\sin^2(\beta)}$$
From this relationship, we can see that as the number of slits $N$ increases,  the secondary maxima compared to the principal maxima must be decreasing, and essentially vanish for large $N$.
But perhaps the argument is easier when we can compare visual scenarios. Look at the following images from hyperphysics.


Using the three and five slit examples of multi-slit interference, we can tell the following:

*

*That as $N$ increases, the principal maxima decrease in width.

*The number of peaks of secondary maxima between each principal maxima is equal to $N-2$.

*As $N$ increases, the intensity of the secondary maxima decrease.

*The resulting principal maxima follow the curve of the single slit scenario.

The last point (4) results from the intensity being a product of an expression for single slit, and an expression for all $N$ slits. $$$$
