Question

A laser tuned to a wavelength of 6.05 x 10 –7 m is shone into a diamond (n = 2.42). What is the beam's wavelength [µm] in the diamond?

Answer 1

Step-by-step explanation:

To calculate the beam's wavelength in the diamond, we can use Snell's Law, which relates the angle of incidence and the refractive indices of two mediums:

n₁ * λ₁ = n₂ * λ₂

Where:

n₁ = refractive index of the initial medium (air or vacuum)

λ₁ = wavelength in the initial medium (given as 6.05 x 10^(-7) m)

n₂ = refractive index of the second medium (diamond, given as 2.42)

λ₂ = wavelength in the second medium (what we want to find)

Rearranging the equation, we can solve for λ₂:

λ₂ = (n₁ * λ₁) / n₂

Given that n₁ is approximately 1 (refractive index of air or vacuum), we can substitute the values:

λ₂ = (1 * 6.05 x 10^(-7) m) / 2.42

Calculating this expression:

λ₂ ≈ 2.50 x 10^(-7) m

To convert this wavelength to micrometers (µm), we divide by 10^(-6):

λ₂ ≈ 0.25 µm

Therefore, the beam's wavelength in the diamond is approximately 0.25 µm.