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A thin glass rod is submerged in oil. (n oil= 1.46 and n glass= 1.5). (Hint: n₁ Sinθ₁ = n₂ Sinθ₂. Think about critical angle) a. What is the critical angle for light traveling inside the rod? b. If you replace the oil with water (n water = 1.33) what will be the critical angle?

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To determine the critical angle, we can use Snell's law, which relates the angles and refractive indices of light passing through different media. The formula is given by:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:
n₁ and n₂ are the refractive indices of the initial and final media, respectively.
θ₁ and θ₂ are the angles of incidence and refraction, respectively.

a) For the thin glass rod submerged in oil:
n₁ (glass) = 1.5
n₂ (oil) = 1.46

Let's assume the critical angle inside the rod is θc. At the critical angle, the angle of refraction becomes 90 degrees (sin(90) = 1). Plugging these values into Snell's law:

1.5 * sin(θc) = 1.46 * sin(90)

Simplifying the equation:
sin(θc) = 1.46 / 1.5
θc = arcsin(1.46 / 1.5)

Using a calculator, we find:
θc ≈ 73.75 degrees

Therefore, the critical angle for light traveling inside the glass rod submerged in oil is approximately 73.75 degrees.

b) If we replace the oil with water:
n₁ (glass) = 1.5
n₂ (water) = 1.33

Using Snell's law, we can again find the critical angle:

1.5 * sin(θc) = 1.33 * sin(90)

sin(θc) = 1.33 / 1.5
θc = arcsin(1.33 / 1.5)

Calculating the value:
θc ≈ 48.6 degrees

Therefore, if we replace the oil with water, the critical angle for light traveling inside the glass rod will be approximately 48.6 degrees.
User David Alvarez
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