How to Calculate the Index of Refraction of a Liquid?
What is the index of refraction of the liquid?
When light in a vacuum is incident on a transparent glass slab at an angle of 32.0° and then the slab is immersed in a pool of liquid with an angle of incidence of 24.0°, the angle of refraction for the light entering the slab is the same as when the slab was in a vacuum. How can we calculate the index of refraction of the liquid?
Answer:
The index of refraction of the liquid can be calculated using Snell's law. By equating the index of refraction of the glass slab in a vacuum with the index of refraction of the liquid, the unknown index of refraction of the liquid can be determined.
To calculate the index of refraction of the liquid, we need to utilize Snell's law, which governs the refraction of light as it passes from one medium to another. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.
Let's denote the index of refraction of a vacuum as n₁ (which is known to be 1), the angle of incidence at 32.0° as θ₁, the index of refraction for the glass slab as n₂, and the angle of refraction as θ₂. By applying Snell's law with the given values, n₁ sin θ₁ = n₂.
When the glass slab is immersed in the liquid, the new indices and angles are denoted as n₃ for the index of refraction of the liquid (the value we are trying to find), the new angle of incidence at 24.0° as θ₃, and the angle of refraction θ₂ remains unchanged. By applying Snell's law again, we get n₃ sin θ₃ = n₂.
By equating the two expressions for n₂, we have n₁ sin θ₁ = n₃ sin θ₃. Solving this equation will give us the index of refraction of the liquid. This methodology allows us to determine the index of refraction of a liquid based on the known values of the incident angles and the index of refraction of the glass slab.
Understanding and applying Snell's law in this context enables us to calculate the index of refraction of the liquid accurately. It showcases the relationship between the angles of incidence and refraction, as well as the indexes of refraction for different media.