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A layer of ethyl alcohol (n = 1.361) is on top of water (n = 1.333). To the nearest degree, at what angle relative to the normal to the interface of the two liquids is light totally reflected?
a. 78 degree
b. 88 degree
c. 68 degree
d. 49 degree
e. the critical angle isundefined

Answer :

hamzaahmeds

Answer:

a. 78 degree

Explanation:

According to Snell's Law, we have:

(ni)(Sin θi) = (nr)(Sin θr)

where,

ni = Refractive index of medium on which light is incident

ni = Refractive index of ethyl alcohol = 1.361

nr = Refractive index of medium from which light is refracted

nr = Refractive index of ethyl alcohol = 1.333

θi = Angle of Incidence

θr = Angle of refraction

So, the Angle of Incidence is know as the Critical Angle (θc), when the refracted angle becomes 90°. This is the case of total internal reflection. That is:

θi = θc

when, θr = 90°

Therefore, Snell's Law becomes:

(1.361)(Sin θc) = (1.333)(Sin 90°)

Sin θc = 1.333/1.361

θc = Sin⁻¹ (0.9794)

θc = 78.35° = 78° (Approximately)

Therefore, correct answer will be:

a. 78 degree

The angle relative to the normal interface of the two liquids at which the light is totally reflected is 78 degrees.

From the information given;

  • the refractive index of the ethyl alcohol [tex]\mathbf{n_1= 1.361}[/tex]
  • the refractive index of the water [tex]\mathbf{n_2 = 1.333}[/tex]
  • the angle of incidence is the critical angle [tex]\theta_i = \theta_c[/tex]
  • the angle of refraction [tex]\theta _r = 90^0[/tex]  

According to Snell's Law of refraction;

[tex]\mathbf{n_1 sin \theta _c = n_2 sin \theta_r}[/tex]

[tex]\mathbf{1.361 \times sin \theta _c = 1.333 \times sin 90}[/tex]

[tex]\mathbf{ sin \theta _c =\dfrac{ 1.333 \times sin 90}{1.361}}[/tex]

[tex]\mathbf{ sin \theta _c =\dfrac{ 1.333 \times 1}{1.361}}[/tex]

[tex]\mathbf{ \theta _c = sin^{-1} (0.9794)}[/tex]

[tex]\mathbf{ \theta _c =78.35^0}[/tex]

[tex]\mathbf{ \theta _c \simeq78^0}[/tex]

Therefore, we can conclude that the angle relative to the normal interface of the two liquids at which the light is totally reflected is 78 degrees.

Learn more about Snell Law of refraction here:

https://brainly.com/question/14029329?referrer=searchResults

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