Astudent and his lab partner create a single slit by carefully aligning two razor blades to a separation of 0.530 mm. when a helium–neon laser at 543 nm illuminates the slit, a diffraction pattern is observed on a screen 1.55 m beyond the slit. calculate the angle θdark to the first minimum in the diffraction pattern and the width of the central maximum.

angle = 0.058699 degree

width of central maximum  is 3.170566 × m

distance D =  1.55 m

wavelength w = 543 nm = 543× m

to find out

angle θ and width of the central maximum

solution

we know according to first condition first dark that mean

wavelength = dsinθ

so put value and find θ

543× = 0.530× ×sinθ

sinθ  =  543× / 0.530×

sinθ   =  1.02452 × [tex]10^{-3}

θ = 0.058699 degree

and

we can say

tanθ = y/D

here y is width of central maximum Y = 2y

put all value we get  y

so y = D tanθ

y = 1.55 (tan0.0586)

y = 1.58528 × [tex]10^{-3} m =

so Y = 2 ( 1.58528 × [tex]10^{-3} )

so width of central maximum  is 3.170566 × [tex]10^{-3} )  m