Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 500-nm thick. Calculate the change of phase of the light that penetrates the front surface, reflects from the second surface, and emerges through the first surface as an angle between 0° and 360°?
A) 280°
B) 160°
C) 220°
D) 100°
E) 290°

Question

Quizplus · Accepted Answer

The phase change upon reflection can be calculated as:
Phase change upon reflection = 2 * (pi) * (thickness of medium) * (refractive index) / (wavelength)
= 2 * pi * 500 nm * 1.4 / 500 nm
= 8.96 * pi radians

Since the light is reflected twice, the total phase change will be twice this value:
Total phase change = 2 * 8.96 * pi radians
= 56.24° (rounded to the nearest degree)

When the light emerges from the first surface of the soap bubble, it undergoes a phase change due to the change in refractive index. This phase change equals pi radians for light going from a lower to a higher refractive index.

Therefore, the total phase change upon emergence from the first surface is given by:
Total phase change = pi + 2 * 56.24°
= 290° (rounded to the nearest degree)

Hence, the answer is (E) 290°.

Monochromatic Light (λ = 500 Nm) Is Incident on a Soap