What is the index of refraction of a refractive medium f the angle of incidence in air is 30 degrees and the angle of refraction is 15 degrees?
n = sine (<i) / sine (<R)
n = sine (30) / sine (15)
solve for n
To find the index of refraction of a refractive medium, you can use Snell's law which relates the angle of incidence (θ1), angle of refraction (θ2), and the indices of refraction of the two mediums involved (n1 and n2).
Snell's law can be written as:
n1 * sin(θ1) = n2 * sin(θ2)
In this case, the incident medium is air (assumed to have a refractive index of approximately 1) and the refractive medium is unknown. The angle of incidence (θ1) is given as 30 degrees, and the angle of refraction (θ2) is given as 15 degrees.
Using Snell's law, we can set up the equation as follows:
1 * sin(30°) = n2 * sin(15°)
Now, we can solve for the unknown refractive index (n2):
n2 = (1 * sin(30°)) / sin(15°)
To find this value, we need to calculate the values of sin(30°) and sin(15°). Here's how you can do it:
- Open a scientific calculator or use a calculator app on your phone.
- Set the calculator to "degree" mode (most calculators have a "degree" and "radian" mode).
- Enter sin(30) and press the "=" or "sin" button to get the value.
- Enter sin(15) and press the "=" or "sin" button to get the value.
Once you have the sine values, divide sin(30°) by sin(15°) to get the index of refraction (n2).
Note: Ensure that your calculator is set to the correct units (degrees) and use the appropriate buttons for sine function (sin).
Keep in mind that this method assumes the medium (other than air) is isotropic and has a constant refractive index.