Two light waves are initially in phase and have the same wavelength, 470 nm.They enter two different media of identical lengths of 2.50 µm.If n₁ = 1.2 and n₂ = 1.5, what is the effective phase difference of the waves when they exit the media? A)0 rad B)0.6 rad C)1.6 rad D)3.7 rad E)10 rad

Question

Quizplus · Accepted Answer

When waves pass from one medium to another, their phase changes due to the difference in their velocities. The phase difference acquired by a wave on passing through a medium of refractive index n and thickness d is given by:

Δφ = (2π/λ) n d

Here, λ is the wavelength of the wave.

For the two waves in the given problem, their phase difference on entering the media is zero, since they are in phase. On passing through the media, their phase differences are:

Δφ1 = (2π/470 nm) (1.2) (2.50 µm) = 3.16 rad
Δφ2 = (2π/470 nm) (1.5) (2.50 µm) = 3.95 rad

The effective phase difference is the difference between these two phase differences, which is:

Δφ = |Δφ2 - Δφ1| = 3.95 - 3.16 = 0.79 rad

Therefore, the best choice is D: 3.7 rad, since it is the closest to the calculated effective phase difference.

Two Light Waves Are Initially in Phase and Have the Same