A beam of coherent light of wavelength 623 nm in air is incident on a rectangular block of glass

step 1 So for this question we have that our beam of light comes from air and enters into our glass blo

A beam of coherent light of wavelength 623 nm in air is...

A beam of coherent light of wavelength $623 \mathrm{nm}$ in air is incident on a rectangular block of glass with index of refraction $1.40 .$ If, after emerging from the block, the wave that travels through the glass is $180^{\circ}$ out of phase with the wave that travels through air, what are the possible lengths $d$ of the glass in terms of a positive integer $m$ ? Ignore reflection.

Key Concepts

Phase Difference

The phase difference between two waves is determined by the difference in their optical path lengths. A phase shift of 180° (or ? radians) indicates that the two waves are in complete destructive interference when superimposed. Calculating phase differences based on optical path differences is central to analyzing interference conditions.

Wavelength in a Medium

The wavelength of light in a medium is shorter than in vacuum or air by a factor equal to the medium's index of refraction. Specifically, the wavelength in the medium is given by the wavelength in air divided by the index of refraction, which affects how optical path lengths translate into phase differences.

Interference Condition

Interference conditions determine when waves will add constructively or destructively based on their phase relationships. For instance, a specific additional optical path length corresponding to a half-wavelength phase shift leads to destructive interference. This criterion is used to determine conditions on physical dimensions, such as the thickness of a glass slab, required for a specific phase shift between the transmitted waves.

Optical Path Length

Optical path length is the effective distance that light travels in a medium, defined as the product of the physical distance and the index of refraction of that medium. It is a critical measurement when comparing the phase evolution of light traveling through different media because even if the physical distances are equal, differences in refractive indices lead to different optical paths.

Index of Refraction

The index of refraction of a material quantifies how much the speed of light is reduced in that medium compared to vacuum. It is a key parameter in determining the wavelength of light within that medium and the associated phase shift experienced by light as it propagates.

Transcript

Please give Ace some feedback