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What angle θ3 does the ray refracted into the water make with the normal to the surface? use 1.33 for the index of refraction of water. g?

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Louli
I have attached a screenshot with the complete question.

Answer:
θ₃ = 27.574°

Explanation:
To answer this question, we will use Snell's law twice.
Part 1: getting θ₂:
We have:
n1 is n of air = 1
n2 is n of glass = 1.58
θ₁ is the incident angle = 38°
θ₂ is the angle of refraction we want to find.
Apply Snell's law to get θ₂ as follows:
n1 sin(θ₁) = n2 sin(θ₂)
1 * sin(38) = 1.58 sin(θ₂)
sin (θ₂) = 0.3896
θ₂ = 22.933°

Part 2: getting θ₃:
We have:
n2 is n of glass = 1.58
n3 is n of water = 1.33
θ₂ is the incident angle = 22.933°
θ3 is the angle of refraction we want to find.
Apply Snell's law to get θ₂ as follows:
n2 sin(θ₂) = n3 sin(θ₃)
1.58 * sin(22.933) = 1.33 sin(θ₃)
sin (θ₃) = 0.462897
θ₂ = 27.574°

Hope this helps :)
Ver imagen Louli

The measurement of angle θ3, the ray refracted into the water made with the normal to the surface is 27.574°.

What is Snell's Law?

The ratio of the sine of the angles of incidence and transmission equals the ratio of the refractive index of the materials at the interface, according to Snell's Law.

In order to answer the question, we will use Snell's law twice.

Let's firstly calculate the value of θ₂, as it is known that

n₁ is n of air = 1,

n₂ is n of glass = 1.58

θ₁ is the incident angle = 38°

θ₂ is the angle of refraction which is needed to be calculated, therefore, using Snell's law we can write,

[tex]n_1 \times sin(\theta_1) = n_2 \times sin(\theta_2)\\\\1 \times sin(38^o) = 1.58 \times sin(\theta_2)\\\\sin (\theta_2) = 0.3896\\\\\theta_2 = 22.933^o[/tex]

Similarly to calculate the value of θ₃, we will repeat the process therefore, we will use Snell's Law again, therefore,

n₂ is n of glass = 1.58

n₃ is n of water = 1.33

θ₂ is the incident angle = 22.933°

θ₃ is the angle of refraction we require.

[tex]n_2\times sin(\theta_2) = n_3 \times sin(\theta_3)\\\\1.58 \times sin(22.933) = 1.33\times sin(\theta_3)\\\\sin (\theta_3) = 0.462897\\\\\theta_3= 27.574^o[/tex]

Hence, the measurement of angle θ3, the ray refracted into the water made with the normal to the surface is 27.574°.

Learn more about Snell's Law:

https://brainly.com/question/10112549