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.