Constructive and destructive interference can be explained in terms of phase and path difference. Interference patterns can be calculated using wavelength, grating spacing and angle of maxima.
When white light is incident on a grating the central maximum is white. Spectra are produced at the other order maxima.
Consider the grating relationship:
for any particular grating \(d\) is constant
for each order maximum \(n\) is the same
Therefore:
\(\sin \theta\) depends only on wavelength
Hence the bigger the wavelength the bigger the angle \(\theta\)
Question
If the brightness of light in a double slit experiment is increased what happens to the fringe spacing (distance between two consecutive maxima or minima)?
There is no change in fringe spacing - this only depends on the wavelength and slit spacing.
If the wavelength of light increases (eg red instead of blue light) the fringe spacing would increase.