Coherent light of wavelength 525 nm passes through two thin slits that are 4.15ã—10^(−2) mm apart and then falls on a screen 75.0 cm away.
part ahow far away from the central bright fringe on the screen is the fifth bright fringe (not counting the central bright fringe)? y5= cm
part bhow far away from the central bright fringe on the screen is the eighth dark fringe? y8= cm

A) 4.7 cm

The formula for the angular spread of the nth-maximum from the central bright fringe for a diffraction from two slits is

where

n is the order of the maximum

is the wavelength

is the distance between the slits

In this problem,

n = 5

So we find

And given the distance of the screen from the slits,

The distance of the 5th  bright fringe from the central bright fringe will be given by

B) 8.1 cm

The formula to find the nth-minimum (dark fringe) in a diffraction pattern from double slit is a bit differente from the previous one:

To find the angle corresponding to the 8th dark fringe, we substitute n=8:

And the distance of the 8th dark fringe from the central bright fringe will be given by

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6 cos 34, 6 sin 34 trig