Chapter 35: Q90P (page 1079)

In Fig 35-54, two isotropic point sources $S_{1}$ and $S_{2}$ emit light at wavelength $λ = 400 nm$ . Source $S_{1}$ is located at $y = 640 nm$ , source $S_{2}$ is located at $y = - 640 nm$ . At point $P_{1}$ (at $x = 720 nm$ ), the wave from $S_{2}$ arrives ahead of the wave from $S_{1}$ by a phase difference of $0.600 π$ rad. (a) What multiple of $λ$ gives the phase difference between the waves from the two sources as the waves from the two sources as the waves arrive at point $P_{2}$ , which is located at $y = 720 nm$ ? (The figure is not drawn to scale) (b) If the waves arrive at $P_{2}$ with equal amplitudes, is the interference there fully constructive, fully destructive, intermediate but closer to fully destructive, intermediate but closer to fully destructive?

Short Answer

Expert verified

Thus,

(a) the wavelength is $2.90 λ$ .

(b) the nature is intermediate.

Step by step solution

Multiple of λ gives phase difference.

(a)

Since $P_{1}$ is equidistant from $S_{1}$ and $S_{2}$ conclude the sources are not in phase with each other. Their phase difference is $Δ ϕ_{S o u r c e} = 0.60 π rad$ , which may be expressed in terms of wavelengths as

$\begin{array}{rcl} Δ ϕ_{S o u r c e} & = & \frac{0.60 π}{2 π} λ \\ = & 0.3 λ \end{array}$

Now, $S_{1}$ is closer to $P_{2}$ than $S_{2}$ is source $S_{1}$ is 80nm from $P_{2}$ while source $S_{2}$ is 1380 nm from $P_{2}$ . Here we find a difference of $Δ ϕ_{P a t h} = 3.2 λ$ . Thus, the net difference is: