What is the distance on the screen from the center of the central maximum to the first minimum?

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Two slits spaced 0.260 mm apart are placed 0.800 m from a screen and illuminated by coherent light with a wavelength of 610 nm. The intensity at the center of the central maximum ( θ =0o) is I0. What is the distance on the screen from the center of the central maximum to the first minimum? What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to I_{0}/2?

Answer

for first minima m=0
m=0

lambda=610*10-9
r=(distance from screen)=.8
d(distance between split)=.26*10^-3

plug in rest of values into

Ym=R((m + 1/2) lambda / d )

(.80*(0+1/2)*610*10^-9)/(.26*10^-3)= (9.4*10^-4) m

the distance on the screen from the center of the central
l maximum to the first minimum is (9.4*10^-4) m

For part two divide the first answer by two to get 4.7*10^-4m!

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