In Fig. 35.27, an airtight chamber of length d=5.0 cm is placed in one of the arms of a Michelso

In Fig. 35.27, an airtight chamber of length d=5.0 cm is...

In Fig. 35.27, an airtight chamber of length $d=5.0$ $\mathrm{cm}$ is placed in one of the arms of a Michelson interferometer. (The glass window on each end of the chamber has negligible thickness.) Light of wavelength $\lambda=500 \mathrm{~nm}$ is used. Evacuating the air from the chamber causes a shift of 60 bright fringes. From these data and to six significant figures, find the index of refraction of air at atmospheric pressure. ( FIGURE CAN'T COPY )

Key Concepts

Index of Refraction

The index of refraction is a measure of how much a medium slows down light compared to its speed in a vacuum. This property is critical in determining the optical path length because it directly scales the physical distance. Measurements of fringe shifts in interferometry experiments can provide accurate values of the refractive index for various materials by relating the observed optical path changes to known physical dimensions.

Interference Fringe Shift

Interference fringe shifts occur when there is a change in the optical path length of one arm of an interferometer. By counting the number of fringe shifts that occur when a medium in one arm is altered (for example, by evacuating air), one can quantitatively determine changes in the optical path length, and from that, deduce properties such as the refractive index of the medium.

Optical Path Length

The optical path length is the product of the physical distance a light beam travels and the refractive index of the medium through which it passes. It determines the phase of the light beam when it interferes with another beam, and any change in either the distance or the refractive index will alter the optical path length, leading to shifts in the interference fringes.

Michelson Interferometer

A Michelson interferometer is an optical instrument that splits a beam of light into two paths, reflects them back, and then recombines them to produce an interference pattern. This interference pattern is highly sensitive to differences in the optical path lengths of the two arms, making the device useful for precision measurements such as changes in refractive index or distance variations.

Transcript

00:01 Okay, so the question was asking us to find the index of refraction of air atmospheric pressure.

00:07 So we have such equation with delta 5 equal 2 pi over lambda times delta lambda equal to 2 pi over landa times 2d times a minus 1.

00:16 Okay, so this is the equation for the relationship between the path difference and the phase difference of light rays.

00:23 Delta phi is the phase difference of light rays.

00:25 Landa is the wavelengths of the light rays.

00:28 And delta landa is the path difference between.

00:31 Between the refracted rate and transmitted rate.

00:35 The reason why delta landa is equal to 2d times n minus 1 is because the path lens for the refracted rate is 2d, and the path difference for the i'm sorry, the path length for the transmitting rate is 2d.

00:53 So the difference between the refractive rate and the transmitted rate is just simply the path length of the refractive rate rate minus the path length of the transmitting rate, which is 2dn minus 2d.

01:09 And we do some arrangement.

01:10 We'll get it's 2d times n minus 1.

01:17 And so we know the fringe pattern of light rays can shift by one fringe for each phase change of light rays.

01:25 Therefore, we can have another expression, which is this expression could be for the phase change of light rays, which is delta 5 is equal to i remember it was 2 pi and delta 5 here is the same thing is the path difference i'm sorry the phase difference of light rays okay delta 5 is the phase difference of light rays and n here is the number of bright ranges so we can say that is two equations to each other equal to each other so we'll get 2 pi over lambda times 2d times n minus 1 equal to 2 pi n.

02:26 Okay, i remember d in this case just the length of the chamber, okay? so if we do some arrangement, because our goal is finding the index of refraction, n.

02:39 So we need to set out n on the left side, okay? let's do some quick arrangement here...

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