To calculate the wavelength of a light ray passing through a transparent medium, we can use Snell's law. Snell's law relates the angles of incidence and refraction, as well as the refractive indices of the two mediums involved. It can also be used to calculate the change in wavelength.
Snell's law is given by:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where: n₁ = refractive index of the first medium (air) = 1 n₂ = refractive index of the second medium (transparent medium) = 1.45 θ₁ = angle of incidence (between the incoming ray and the normal) θ₂ = angle of refraction (between the refracted ray and the normal)
In this case, we're assuming the incident ray is perpendicular to the surface (θ₁ = 0). Therefore, the angle of refraction (θ₂) will also be 0.
Using Snell's law, we can solve for the sin(θ₁):
1 * sin(0) = 1.45 * sin(0) 0 = 0
Since the sin(θ₁) is 0, it means that the incident ray passes directly through without deviating or refracting.
Hence, the wavelength of the light ray in the transparent medium will be the same as in the air, which is 5×10^(-7) m.