Question

Two flat glass surfaces are separated by a 150-nm gap of air.

A) What wavelength light illuminating the air gap is reflected brightly?

Answer 1

The bright reflection of light occurs due to the phenomenon of interference. When light waves reflect off two flat surfaces separated by a small gap, constructive interference can occur, resulting in bright reflection.

Step-by-step explanation:

The bright reflection of light occurs due to the phenomenon of interference. When light waves reflect off two flat surfaces separated by a small gap, constructive interference can occur, resulting in bright reflection. The condition for constructive interference is given by the equation:

2d = mλ

Where:

d is the gap between the glass surfaces

m is an integer representing the order of the bright reflection

λ is the wavelength of the incident light

For the 150 nm air gap, the condition for bright reflection would be:

2(150 nm) = mλ

From this equation, we can find the wavelength, λ, that would result in a bright reflection.

Answer 2

The wavelength of light that is reflected brightly in the air gap between two flat glass surfaces can be determined using the concept of interference. The condition for constructive interference is that the path difference between the two reflected waves is equal to an integer multiple of the wavelength. Therefore, there are infinitely many wavelengths of light that can satisfy this condition.

Step-by-step explanation:

The wavelength of light that is reflected brightly in the air gap between two flat glass surfaces can be determined by using the concept of interference. When light passes through a medium with a different refractive index, some of it will be reflected back. Constructive interference occurs when the reflected waves add up to create a brighter reflection.

The conditions for constructive interference are met when the path difference between the two reflected waves is an integer multiple of the wavelength. In the case of an air gap, the path difference is twice the thickness of the air gap. Therefore, the condition for constructive interference is:

2d = mλ

where d is the thickness of the air gap, λ is the wavelength of light, and m is an integer representing the order of the interference.

For the air gap to reflect brightly, we want the condition for constructive interference to be satisfied. We can rearrange the equation to solve for the wavelength:

λ = 2d/m

where m can be any positive integer. Therefore, there are infinitely many wavelengths of light that can satisfy this condition. However, if we want the reflection to be particularly bright, we can choose values of m that yield large values of λ. For example, if we choose m = 1, the wavelength of light that will reflect brightly is equal to twice the thickness of the air gap.