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A tank holds a 1.44-m thick layer of oil that floats on a 0.98-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.40 and 1.52, respectively. A ray originating at O crosses the brine-oil interface at a point 0.7 m from the axis. The ray continues and emerges into the air above the oil. What is the angle that the ray in the air makes with the vertical axis

Respuesta :

Answer:

Angle of ray makes with the vertical is 62.1 degree

Explanation:

As per the ray diagram we know that the angle of incidence on oil brine interface will be given as

[tex]tan\theta_i = \frac{0.7}{0.98}[/tex]

[tex]\theta_i = 35.5^0[/tex]

now by Snell'a law at that interface we have

[tex]\mu_1 sin\theta_i = \mu_2 sin \theta_r[/tex]

now we will have

[tex]1.52  sin35.5 = 1.40 sin\theta_r[/tex]

[tex]\theta_r = 39.12^0[/tex]

now this is the angle of incidence for oil air interface

so now again by Snell's law we will have

[tex]\mu_2 sin\theta_i' = \mu_{air} sin\theta[/tex]

[tex]1.40 sin39.12 = 1 sin\theta[/tex]

[tex]\theta = 62.1^0[/tex]

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