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AS physics diffraction question!

I know that there are four factors that affect diffraction angle in youngs double slit experiment,
1) Wavelength
2) slit separation
3) fringe spacing
4) distance to the fringes

For very small angles tan and sine are approximately equal, so X(fringe separation)/L(distance)=landa/d (slit separation)

But sometimes questions like, "if you double the wavelength and half the slit separation what happens to the angle?" or "what happens to angle if slit separation is doubled and distance to fringes is halved" or "if wavelength increases and the fringe separation is halved, what happens to angle of diffraction" THROW ME OFF.

Please help me understand the relationship between them.

Reply 1

Dowel

Original post by ehlamleyla

This is what I think but I'm not completely sure

You need to remember that nlanda = dsintheta always works for any diffraction grating/ slit combination. As you say for small angles X/L = landa/d. We also know by using trigonometry that sin theta = nlanda/d and tan theta = X/L

so for the first example double the wavelength and half d you get sin theta = n2landa/0.5d so the fraction is bigger and this means sin theta is bigger so theta must also be bigger as arcsine of nlanda/d is < n2landa/0.5d

This is all you need to do for these questions, either that or just know what happens in each case.