A beam of light wavelenght 560 to availing in air is incident on a surface of a transparent material. The incident beam makes an angle of 65degree with the normal and the refracted beam makes an angle of 45degree with the normal.

calculate the refractive index of the material.

Use Snells Law. We will be happy to critique your work.

To calculate the refractive index of the 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 is given by:

n₁ * sin(θ₁) = n₂ * sin(θ₂),

where n₁ is the refractive index of the initial medium (in this case, air), and n₂ is the refractive index of the material.

Given information:
- Wavelength of light in air = 560 nm = 560 × 10^(-9) m
- Angle of incidence (θ₁) = 65 degrees
- Angle of refraction (θ₂) = 45 degrees

First, let's convert the angles from degrees to radians:

θ₁ = 65 degrees × (π/180) = 1.13446 radians
θ₂ = 45 degrees × (π/180) = 0.78539 radians

Next, substitute the values into Snell's law:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

In this case, the refractive index of the initial medium (n₁) is 1 (since air is usually considered to have a refractive index of approximately 1).

1 * sin(1.13446) = n₂ * sin(0.78539)

Solving for n₂:

n₂ = sin(1.13446) / sin(0.78539)

Using a scientific calculator:

n₂ ≈ 1.493

Therefore, the refractive index of the material is approximately 1.493.