Question

Light of unknown wavelength shines on a precisely machined wedge of glass with refractive index 1.52. The closest point to the apex of the wedge where reflection is enhanced occurs where the wedge is 92 nm thick

Part A
Find the wavelength.

Answer 1

The calculated wavelength within the medium is approximately 279.68 nm, and the wavelength in air is approximately 184 nm.

Step-by-step explanation:

The student is asking to find the wavelength of light that enhances reflection at the closest point to the apex of a glass wedge, given the thickness and refractive index. To solve this, we apply the principle of constructive interference, where the path difference between the reflected light waves should be an integral multiple of the wavelength within the medium. The thickness of the wedge where the reflection is enhanced is 92 nm, and the refractive index is 1.52.

The condition for constructive interference is:

2 × (thickness of the wedge) × (refractive index) = m × wavelength

Where 'm' is the order of the fringe, which is 1 for the first bright fringe. Plugging in the values:

2 × 92 nm × 1.52 = 1 × wavelength

wavelength = 2 × 92 nm × 1.52 = 279.68 nm within the medium.

To find the wavelength in air, we divide by the refractive index:

wavelength in air = 279.68 nm / 1.52 ≈ 184 nm