A beam of light of wavelength 550nm travelling in air is incident on a surface of transparent material. The incident beam makes an angle of 60 degree with the normal and the refracted beam makes an angle of 45 degree with the normal. Calculate the refractive index of the material
To calculate the refractive index of the material, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two media.
Snell's law states:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
where:
- n₁ is the refractive index of the initial medium (in this case, air)
- θ₁ is the angle of incidence
- n₂ is the refractive index of the material
- θ₂ is the angle of refraction
In this case, we know the following values:
- n₁ = 1 (refractive index of air)
- θ₁ = 60 degrees
- θ₂ = 45 degrees
Plugging these values into Snell's law:
1 * sin(60) = n₂ * sin(45)
Simplifying the equation:
sin(60) = n₂ * sin(45)
Now we can solve for n₂:
n₂ = sin(60) / sin(45)
Using a calculator:
n₂ ≈ 1.414
Therefore, the refractive index of the material is approximately 1.414.