Single slit and double slit interference

Question

I skimmed this and this about the title subject but I am still unclear. What are the differences and similarities between single slit and double slit interference patterns?

Answer 1

The expressions for single slit and double slit Fraunhofer diffraction look like:

$$I(\theta )=I(0)\ \text{sinc}^2\beta$$ $$I(\theta)=I(0)\ (\text{sinc}^2\beta)(\cos^2\alpha)$$ where $\alpha=(\pi a\sin\theta)/\lambda$ and $\beta=(\pi b\sin\theta)/\lambda$ and as usual $a$ and $b$ represent the distance between the slits and width of slits. Also

$$\text{sinc}( u)\equiv\frac{\sin u}{u}$$

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OP is asking for the similarity and difference between the patterns. Now These are two different functions but you can plot them to see what are differences and similarity. This task, I left, to OP. :) You can find the plot here. Focus on envelope for similarity.

Answer 2

Take a look at single edge Diffraction patterns: https://images.app.goo.gl/RSYzmToh96thgAfM6

A single slit has two edges with diffraction patterns going opposite directions. A double slit has four edges with diffraction patterns going opposite directions and overlapping each other.