The angle of incidence of light passing from air to a liquid is 38 degrees.The angle of refraction is 24.5 degrees. What is the index of refraction of the liquid

n =sini/sinr =

= sin 38/sin24.5=
= 0.616/0.415 =1.48

The index of refraction of a medium can be calculated using Snell's law, which relates the angle of incidence (θ1), the angle of refraction (θ2), and the indices of refraction of the two media (n1 and n2).

Snell's law is given by:
n1 * sin(θ1) = n2 * sin(θ2)

Given that the angle of incidence (θ1) is 38 degrees and the angle of refraction (θ2) is 24.5 degrees, we can calculate the index of refraction (n2) of the liquid.

Let's plug in the values into Snell's law and solve for n2:

n1 * sin(θ1) = n2 * sin(θ2)

Assuming that the light is passing from air to the liquid, the index of refraction of air (n1) is approximately 1.

1 * sin(38) = n2 * sin(24.5)

0.6157 = n2 * 0.4030

Dividing both sides by 0.4030:

n2 = 0.6157 / 0.4030

n2 ≈ 1.528

Therefore, the index of refraction of the liquid is approximately 1.528.

To find the index of refraction (n) of a liquid, we can use Snell's law:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:
- n₁ is the index of refraction of the medium the light is coming from (in this case, air)
- θ₁ is the angle of incidence (the angle between the incoming light ray and the normal to the surface of separation)
- n₂ is the index of refraction of the medium the light is entering (in this case, the liquid)
- θ₂ is the angle of refraction (the angle between the refracted light ray and the normal to the surface of separation)

Given:
- θ₁ (angle of incidence) = 38 degrees
- θ₂ (angle of refraction) = 24.5 degrees

First, we need to convert the angles from degrees to radians using the formula:
radians = degrees * π / 180

So, for θ₁:
θ₁ = 38 * π / 180

And for θ₂:
θ₂ = 24.5 * π / 180

Now, we need to rearrange Snell's law to solve for the index of refraction of the liquid (n₂):

n₂ = (n₁ * sin(θ₁)) / sin(θ₂)

Since the light is passing from air to a liquid, the index of refraction of air (n₁) is approximately 1 (often treated as 1 for simplicity).

n₂ = (1 * sin(θ₁)) / sin(θ₂)

Now, substitute the values of θ₁ and θ₂ into the equation and solve for n₂:

n₂ = (sin(38 * π / 180)) / sin(24.5 * π / 180)

Using a calculator, evaluate the expression and you will get the index of refraction of the liquid.