E is the correct answer, and I understand that there is no phase change, but how
ID: 1489345 • Letter: E
Question
E is the correct answer, and I understand that there is no phase change, but how did they conclude that the angle is 290? Please show calculations.
Monochromatic light ( = 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. Express the phase change as an angle between 0° and 360° Assume that the incidence is normal to the surface and keep two significant figures in your answer.
a. 280°
b. 160°
c. 220°
d. 100°
e. 290°
Explanation / Answer
the light has to travel the entire soap bubble thickness and then travel the same distance back to the first surface.
hence total path difference between the light that is reflected right away at the first surface and the light that travels till the second surface and then comes back to the first surface=2*thickness of the soap bubble=1000 nm
now, as speed of light dcreases in side a medium with refractive index greater than 1,
and as speed=frequency*wavelength
and as frequency of a light wave does not change in the medium, wave length is directly proportional to speed of light.
hence as speed becomes (1/n) times the speed of light in free space, wave length also becomes (1/n) times its original wavelength.
hence new wavelength=(500/1.4) nm
then path difference/wave length=2*500/(500/1.4)=2.8
as 1 complete wavelength means 360 degree phase change, 2.8 times the wave length of path difference will mean 2.8*360=1008 degrees of phase change
as phase is repetitive after 360 degrees, actual phase change=1008-360*2=288 degrees
the closest answer is 290 degrees
hence option e is correct.
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