What changes the fringes and what changes the contrast
Fringe separation depends only on λ, D and a. Increasing D or λ, or decreasing a, widens the fringes. Contrast depends on how equal the two amplitudes are: covering one slit partly makes the bright fringes less bright and the dark fringes brighter because destructive interference is now incomplete, so contrast falls with no change in spacing. Increasing the source intensity changes neither the spacing nor the contrast, only the overall brightness.
x = λD/a · contrast set by A₁ vs A₂ · I ∝ A²What this actually means
Split every one of these questions into two answers: what happens to spacing (use x = λD/a) and what happens to contrast or brightness (use amplitude reasoning). Doing both is what earns full marks.
Increasing D widens the fringes but also dims them, because the light is spread over a bigger area and intensity falls with distance. Say both.
Reducing the light through one slit is the classic contrast question. Answer it as: the two amplitudes are now unequal, so destructive interference is incomplete, so the dark fringes are no longer completely dark and contrast is reduced. Spacing is unchanged.
Making both slits narrower (keeping a fixed) reduces the amplitude from each slit so the whole pattern dims, but the extra diffraction widens the envelope so more fringes become visible. Spacing is still unchanged.
Putting a thin transparent sheet over one slit shifts the whole pattern sideways without changing the spacing, because it adds a constant extra optical path to one beam only.
Saying reduced intensity through one slit changes the fringe spacing. It changes only the contrast.
Prove it — watch it be true
- Note the fringe spacing and the depth of the minima with both sources at equal amplitude.
- Reduce one source amplitude and confirm the minima rise off zero while the spacing readout is unchanged.
- Increase D and confirm the spacing grows while the peak intensity falls.