calculate refractive index of a material if the incident ray is two third the reflected ray which is 60°?
To calculate the refractive index of a material, we can use Snell's law, which relates the angle of incidence (θ1), the angle of refraction (θ2), and the refractive index (n) of the material.
Snell's Law states:
n = sin(θ1) / sin(θ2)
In this case, we are given that the reflected ray is 60°. Let's assume the angle of incidence is θ1 and the angle of refraction is θ2.
We are also given that the incident ray (θ1) is two-thirds the angle of the reflected ray. Therefore, we can express θ1 as:
θ1 = (2/3) * 60°
θ1 = 40°
Now, we can substitute the values into Snell's law:
n = sin(40°) / sin(60°)
To calculate the refractive index, we need to know the value of sin(40°) and sin(60°). Using a scientific calculator, we can find the sine values:
sin(40°) ≈ 0.6428
sin(60°) = 0.8660
Now, substitute these values back into Snell's law:
n = 0.6428 / 0.8660
Using a calculator or dividing these values gives us the refractive index:
n ≈ 0.7429
Therefore, the refractive index of the material is approximately 0.7429.