Light enters a container of liquid at an angle of 35° to the normal; the refracted beam makes an angle of 21° with the normal. Calculate the index of refraction of this liquid.
To calculate the index of refraction of the liquid, we can use Snell's law. Snell's law relates the angle of incidence (the angle at which light enters a medium) and the angle of refraction (the angle at which light leaves the medium) to the indices of refraction of the two media.
The formula for Snell's law is:
n1 * sin(θ1) = n2 * sin(θ2)
Where:
- n1 is the index of refraction of the first medium
- n2 is the index of refraction of the second medium
- θ1 is the angle of incidence
- θ2 is the angle of refraction
In this case, the light is entering the liquid, so the first medium is air (assume its index of refraction to be 1 since it is close to a vacuum). The index of refraction of the liquid is what we need to find.
Given:
- θ1 = 35° (angle of incidence)
- θ2 = 21° (angle of refraction)
- n1 = 1 (index of refraction of air)
Let's substitute the given values into Snell's law and solve for n2:
1 * sin(35°) = n2 * sin(21°)
To get the index of refraction, we rearrange the equation to solve for n2:
n2 = (sin(35°)) / (sin(21°))
Now we can calculate:
n2 ≈ 1.455
Therefore, the index of refraction of the liquid is approximately 1.455.