Question

Part D In talking about interference, particularly with light, you will most likely speak in terms of phase differences, as well as wavelength differences. In the mathematical description of a sine wave, the phase corresponds to the argument of the sine function. For example, in the function y=Asin(kx)y=Asin⁡(kx), the value of kxkx at a particular point is the phase of the wave at that point. Recall that in radians a full cycle (or a full circle) corresponds to 2π2π2 pi radians. How many radians would the shift of half a wavelength from the previous part correspond to? Express your answer in terms of ππpi.

Answer 1

θ = π / 2

Step-by-step explanation:

In the interference phenomenon the process is described by the equations

d sin θ = m λ for constructive interference and

d sin θ = (m + 1/2) λ for destructive interference

m is an integer that represents the position of the interference m = 0 for this case the first maximum occurs in

d sin θ = 0

for m=1

sin θ = λ/d

that is, the angle is

θ = 0

the first point of destructive interference is

d sin θ = ½ λ

sin θ = ½ λ/ d

for this value to be maximum the angle of the sine function is

sin θ = +1

θ = π / 2

this is the angle to have destructive interference, this is that there is no line at the point