# Double slit diffraction

In the intensity pattern of double slit there are two terms one for single slit diffraction $$\sin^2a/a^2$$ and another is double slit interference $$\cos^2b$$.In the intensity pattern of double slit diffraction the two terms are multiplied which comes from standard derivation given in text book of optics.

My question is why the two terms are not added rather than multiplied, physically. Please explain intuitively.

• Why would you expect them to be added? – Emilio Pisanty Apr 9 at 12:20
• Actually my teacher asked me such a question in viva – Sourav Rudra Apr 9 at 12:40
• You say that you have a derivation. How does it go? I suspect the associative property is used. By the way, "terms" add up and "factors" multiply. – my2cts Apr 9 at 14:30
• "Why isn't physics like (-------)?" is not a good question. They are multiplied because that's what the calculation comes to. They are not combined through some other operation (addition, exponentiation, the sine of one times a Bessel function over the other, whatever else you might think of) because those operations are not what the calculation produces. Asking why the calculation produces what it produces instead of something else is essentially pointless. – Emilio Pisanty Apr 9 at 16:44
• However, that said, there is a question to be phrased in terms of why is it that it would be a plausible outcome for certain other operations (say, addition) to be the result, and what is it about the deeper structure of the problem that enforces those specific aspects of the result, but they're mostly to probe your understanding of the problem as a whole, and not really something that can be truly answered within this site's format. – Emilio Pisanty Apr 9 at 16:46