Question

Light of wavelength 420 nm is incident normally on a film of water 1.0 µm thick. The index of refraction of water is 1.33.

(a) What is the wavelength of the light in the water?


(b) How many wavelengths are contained in the distance 2t, where t is the thickness of the film? (Do not round your answer to a whole number.)


(c) What is the phase difference between the wave reflected from the top of the air-water interface and the one reflected from the bottom of the water-air interface in the region where the two reflected waves superpose?

Light of wavelength 420 nm is incident normally on a film of water 1.0 um thick. The index of refraction of water is 1.33. (a) What is the wavelength of the light in the water? 315.8 ✓ nm (b) How many wavelengths are contained in the distance 2t, where t is the thickness of the film? (Do not round your answer to a whole number.) 6.33 (c) What is the phase difference between the wave reflected from the top of the air-water interface and the one reflected from the bottom of the water-air interface in the region where the two reflected waves superpose? pi X rad eBook

Please help with part C on this problem. Thank you!

Answer 1

given

wavelength is $\lambda$ = 420 nm

= 420 x 10^-9 m

thickness t = 1.0 µm

= 10^-6 m

refraction index of the water is n = 1.33

a )

$\lambda$_n = $\lambda$ / n

= 420 x 10^-9 / 1.33

$\lambda$_n = 315.789 x 10^-9 m

$\lambda$_n = 315.789 nm

or

the wavelength of the light in the water is $\lambda$ _n = 315.8 nm ( rounded off value )

b )

N = 2 t / $\lambda$ _n

= 2 x 10^-6 / 315.789 x 10^-9

the number of wavelengths are contained in the distance 2t is N = 6.3333

c )

the phase difference is $\delta$ = $\pi$ + 2 N $\pi$

= $\pi$ + 2 x 6.333 x $\pi$

= $\pi$ + 12.666 x $\pi$

= $\pi$ + 12.666 $\pi$

$\delta$ = 13.666 $\pi$ rad

the phase difference between the wave reflected from the top of the air-water interface

and the one reflected from the bottom of the water-air interface in the region where

the two reflected waves superpose is $\delta$ = 13.666 $\pi$ rad