Suppose light strikes a single slit of width a at an angle beta from the perpend

Question

Suppose light strikes a single slit of width a at an angle beta from the perpendicular direction as shown in the diagram. View of slit for (a) and (b): View of slit and screen for part (b): (a) Find the conditions on the angle theta for destructive interference. (If you define a variable that can take discrete values, specify what those values are.) (b) Suppose a screen is placed parallel to the slit at a perpendicular distance L away from the slit. Let y = 0 be the point on the screen immediately across from the center of the slit. Find an expression for y, the position of the central bright maximum of the diffraction pattern.

Explanation / Answer

a) the condition for destrutive interference is sin(theta) = m*lamda/a

lamda is the wavelength of light

n is the order of the interference

then

theta = sin^(-1)*(n*lamda/a)

if theta is small

then

theta = n*lamda/a

b) for first order bright fringes ,n = 1

sin(theta) = 1*lamda/a

but from the figure sin(theta) = y/L

y/L= lamda/a

y =lamda*L/a

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