How Do You Find the Critical Angle of Water?

To find the critical angle of water, you calculate the inverse sine of the ratio of the refractive index of the medium light is entering (like air) to the refractive index of water.

Understanding the Critical Angle

The critical angle is a concept in optics related to total internal reflection. When light travels from a denser medium (like water) to a less dense medium (like air), it bends away from the normal. As the angle of incidence increases, the angle of refraction also increases. The critical angle (often denoted as 𝜃c) is the specific angle of incidence in the denser medium at which the refracted ray travels along the boundary between the two media. If the angle of incidence exceeds the critical angle, the light is entirely reflected back into the denser medium – this is total internal reflection.

The Formula for the Critical Angle

The critical angle (𝜃c) between two media can be found using Snell's Law. When the angle of refraction is 90 degrees (the critical angle), the formula simplifies to:

sin(𝜃c) = n₂ / n₁

Where:

• 𝜃c is the critical angle.
• n₁ is the refractive index of the medium the light is traveling from (the denser medium, e.g., water).
• n₂ is the refractive index of the medium the light is traveling to (the less dense medium, e.g., air).

Calculating the Critical Angle for Water (to Air)

The most common scenario for the critical angle of water involves light passing from water into air.

1. Identify the Refractive Indices:

   • Refractive index of air (n₂): Approximately 1.00
   • Refractive index of water (n₁): Approximately 1.33

   Medium	Refractive Index (n)
   Air	1.00
   Water	1.33

2. Apply the Formula:
   Substitute the values into the critical angle formula:
   sin(𝜃c) = 1.00 / 1.33

3. Calculate the Inverse Sine:
   To find the angle 𝜃c, you take the inverse sine (arcsin or sin⁻¹) of the ratio:
   𝜃c = arcsin(1.00 / 1.33)

Based on the provided information: "𝜃 sub c then equals the inverse sin of 1.00 divided by 1.33."

4. Determine the Angle:
   Performing this calculation: "Entering this expression on our calculator and rounding the result to the nearest degree, we get 49 degrees. This is the critical angle for light that travels through water and is incident on a water–air interface."

Therefore, the critical angle for light traveling from water to air is approximately 49 degrees.

Key Takeaways

• The critical angle depends on the refractive indices of both media involved.
• It only exists when light travels from a denser medium to a less dense medium.
• For water to air, the critical angle is about 49 degrees.
• If light hits the water-air surface from below at an angle greater than 49 degrees, it undergoes total internal reflection.