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英语代写-V00910618

时间：2021-03-04

2021/2/3 Xinyu Wang

V00910618

Experiment 6

Interferometry

Abstract: Michelson Interferometer is important in model physics. It is designed for

Michelson-Morley Experiment to verify the principle of constant speed of light. The

Interferometer is used to generate interference fringes. By studying the change of

interference fringes, we could do some research on refractive index of different objects.

Introduction and Theory:

Interferometers produce interference

patterns by the division and recombination of

light. A sketch of the essential parts of a

Michelson interferometer is shown in Figure

1.

Light from source S is divided into two

paths at the beam splitter A by the partially

silvered front surface mirror. One beam

passes through A to fixed mirror M2 while

the other reflects from A, through the

compensator plate C, to mirror M1. Referring

to Figure 1, on reflection from mirrors M1

and M2 the beams retrace their paths to A

where they recombine to form interference

fringes.

When the compensator plate is used, the

light has the same path length in glass in each

arm of the interferometer (since the plates A

and C are identical in thickness and are

parallel). The difference in the path of the

two beams is then said to be entirely “in-air”.

If the Michelson interferometer is used in

conjunction with a monochromatic source,

such as a sodium lamp or the green line of a

mercury lamp, interference fringes are found

to exist over a path length difference of a few

centimeters. As the path length difference is

gradually increased, the contrast of the

fringes diminishes and finally the fringes

disappear. The fringes eventually vanish

when the difference in path length exceeds

the predominant coherence path length of the

source. Thus, for fringes to be visible, there

must not be an independent change in phase

of the light wave train in either path. The

laser, on the other hand, is said to have a

temporal coherence or coherence path length

orders of magnitude longer than any other

source.

Referring to Figure 1, to have a change of one

fringe requires a change in path length

between the rays to M1 and M2 of one

wavelength. For a change of n fringes,

2 = (1)

Where 2 is the path difference for a

change of fringes and is the

wavelength in air.

Apparatus:

Fig 1

Apparatus(1)

Apparatus(2)

The length of vacuum cell

Procedure:

Use the equation (1) and we know that

wavelength of the He-Ne laser is 632.8nm.

So the value of 2 for a count of 100 fringes

is

2 = 100 × 632.8 = 632.8 × 10−7

The path difference for a count of 100

fringes is

62.1 × 5.09 × 10−7 = 316.089 × 10−7

The reading of the gear ratio is 62.3. So

2 determined from the gear ratio is

2 = 632.178 × 10−7

I think the value above which is 632.8 ×

10−7 is more accurate. eecause the

refractive index of air is not 1, though we

often take it as 1. The refractive index of

vacuum is 1. We should use equation (3)

added the refractive index of air to calculate

the path difference,

2 = (3)

Where = index of refraction of air.

To determine the refractive index of air,

use the equation (2),

2( − 1) = (2)

where,

= wavelength of the laser light in vacuum

= number of fringes observed

= length of path through the cell (to be

measured with travelling microscope).

The length of path through the cell is measure,

= 51.28

The laser light in vacuum is He-Ne laser. The

wavelength of the laser light is,

= 632.8

In experiment, we could see 44 fringes. In

this case = 44.

So,

=

2

+ 1

=

44 × 632.8

2 × 51.28

+ 1 ≈ 1.00027

Use equation (3),

2 = (3)

Where,

2 = 2 × 1.00027 × 316.089 × 10−7

= 632.35 × 10−7

The error could be represented by,

= (632.8 − 632.35) ÷ 632.8 × 100%

= 0.07%

eecause reading the gear ratio has an error,

= 0.1 ÷ 62.3 × 100% = 0.16%

The calculated error is less than the reading

error. We could consider the previous

calculation result to be correct.

Discussion and Question:

Derive equation (2)

2( − 1) = (2)

Where,

= index of refraction of air

= wavelength of the laser light in vacuum

= number of fringes observed

= length of path through the cell (to be

measured with travelling microscope).

The refractive index of vacuum could see

as 1. eecause the path difference is caused by

the difference of the refractive index of air

and vacuum, which could be represented by,

2( − 1)

It could be seemed as 2. Use equation (1).

We have equation (2),

2( − 1) = (2)

The different path has two values,

theoretical value and measurements. The

theoretical value is more accurate. eecause

the value we measured contains a lot of errors

and something should be corrected. In the

initial calculation, we use the equation (1)

which ignores the refractive index of air .

In fact, the thickness of mirrors should be

considered also. If we use the same mirrors,

the influence of the thickness of mirrors

could be ignored. eecause the rays to M1 and

M2 travel the same length in mirrors.

The errors could be concluded as three

points. First, the scale value of the instrument

will cause error. It just depends on the

accuracy of the instrument. Second, what we

read from gear ratio has an error about ±0.5.

If we use the length as the unit to express the

error, it could be ±0.5 × 5.09 × 10−7 .

The influence of this error could be reduced

by increasing the number of fringes we count.

In the above calculation, we only count 100

fringes. The relative error could be smaller, if

we count 200 fringes or more fringes. Third,

the reading of the gear ratio has an accidental

error. We should read the gear ratio more

times and more different 100 fringes to

reduce the error.

Conclusion:

This lab uses interference equation to

calculate the refractive index of air. The

result of calculation of path difference

in theory is different from the path

difference which we get from reading the

gear ratio. We could infer that there is

something wrong. Because the refractive

index of air is ignored. We could use

equation (2) to calculate the refractive

index of air. The result is very close to

the theoretical value. However, the

accuracy of experiment is not high enough.

The result has an error, which is

inevitable, compared with the theoretical

value.

学霸联盟

V00910618

Experiment 6

Interferometry

Abstract: Michelson Interferometer is important in model physics. It is designed for

Michelson-Morley Experiment to verify the principle of constant speed of light. The

Interferometer is used to generate interference fringes. By studying the change of

interference fringes, we could do some research on refractive index of different objects.

Introduction and Theory:

Interferometers produce interference

patterns by the division and recombination of

light. A sketch of the essential parts of a

Michelson interferometer is shown in Figure

1.

Light from source S is divided into two

paths at the beam splitter A by the partially

silvered front surface mirror. One beam

passes through A to fixed mirror M2 while

the other reflects from A, through the

compensator plate C, to mirror M1. Referring

to Figure 1, on reflection from mirrors M1

and M2 the beams retrace their paths to A

where they recombine to form interference

fringes.

When the compensator plate is used, the

light has the same path length in glass in each

arm of the interferometer (since the plates A

and C are identical in thickness and are

parallel). The difference in the path of the

two beams is then said to be entirely “in-air”.

If the Michelson interferometer is used in

conjunction with a monochromatic source,

such as a sodium lamp or the green line of a

mercury lamp, interference fringes are found

to exist over a path length difference of a few

centimeters. As the path length difference is

gradually increased, the contrast of the

fringes diminishes and finally the fringes

disappear. The fringes eventually vanish

when the difference in path length exceeds

the predominant coherence path length of the

source. Thus, for fringes to be visible, there

must not be an independent change in phase

of the light wave train in either path. The

laser, on the other hand, is said to have a

temporal coherence or coherence path length

orders of magnitude longer than any other

source.

Referring to Figure 1, to have a change of one

fringe requires a change in path length

between the rays to M1 and M2 of one

wavelength. For a change of n fringes,

2 = (1)

Where 2 is the path difference for a

change of fringes and is the

wavelength in air.

Apparatus:

Fig 1

Apparatus(1)

Apparatus(2)

The length of vacuum cell

Procedure:

Use the equation (1) and we know that

wavelength of the He-Ne laser is 632.8nm.

So the value of 2 for a count of 100 fringes

is

2 = 100 × 632.8 = 632.8 × 10−7

The path difference for a count of 100

fringes is

62.1 × 5.09 × 10−7 = 316.089 × 10−7

The reading of the gear ratio is 62.3. So

2 determined from the gear ratio is

2 = 632.178 × 10−7

I think the value above which is 632.8 ×

10−7 is more accurate. eecause the

refractive index of air is not 1, though we

often take it as 1. The refractive index of

vacuum is 1. We should use equation (3)

added the refractive index of air to calculate

the path difference,

2 = (3)

Where = index of refraction of air.

To determine the refractive index of air,

use the equation (2),

2( − 1) = (2)

where,

= wavelength of the laser light in vacuum

= number of fringes observed

= length of path through the cell (to be

measured with travelling microscope).

The length of path through the cell is measure,

= 51.28

The laser light in vacuum is He-Ne laser. The

wavelength of the laser light is,

= 632.8

In experiment, we could see 44 fringes. In

this case = 44.

So,

=

2

+ 1

=

44 × 632.8

2 × 51.28

+ 1 ≈ 1.00027

Use equation (3),

2 = (3)

Where,

2 = 2 × 1.00027 × 316.089 × 10−7

= 632.35 × 10−7

The error could be represented by,

= (632.8 − 632.35) ÷ 632.8 × 100%

= 0.07%

eecause reading the gear ratio has an error,

= 0.1 ÷ 62.3 × 100% = 0.16%

The calculated error is less than the reading

error. We could consider the previous

calculation result to be correct.

Discussion and Question:

Derive equation (2)

2( − 1) = (2)

Where,

= index of refraction of air

= wavelength of the laser light in vacuum

= number of fringes observed

= length of path through the cell (to be

measured with travelling microscope).

The refractive index of vacuum could see

as 1. eecause the path difference is caused by

the difference of the refractive index of air

and vacuum, which could be represented by,

2( − 1)

It could be seemed as 2. Use equation (1).

We have equation (2),

2( − 1) = (2)

The different path has two values,

theoretical value and measurements. The

theoretical value is more accurate. eecause

the value we measured contains a lot of errors

and something should be corrected. In the

initial calculation, we use the equation (1)

which ignores the refractive index of air .

In fact, the thickness of mirrors should be

considered also. If we use the same mirrors,

the influence of the thickness of mirrors

could be ignored. eecause the rays to M1 and

M2 travel the same length in mirrors.

The errors could be concluded as three

points. First, the scale value of the instrument

will cause error. It just depends on the

accuracy of the instrument. Second, what we

read from gear ratio has an error about ±0.5.

If we use the length as the unit to express the

error, it could be ±0.5 × 5.09 × 10−7 .

The influence of this error could be reduced

by increasing the number of fringes we count.

In the above calculation, we only count 100

fringes. The relative error could be smaller, if

we count 200 fringes or more fringes. Third,

the reading of the gear ratio has an accidental

error. We should read the gear ratio more

times and more different 100 fringes to

reduce the error.

Conclusion:

This lab uses interference equation to

calculate the refractive index of air. The

result of calculation of path difference

in theory is different from the path

difference which we get from reading the

gear ratio. We could infer that there is

something wrong. Because the refractive

index of air is ignored. We could use

equation (2) to calculate the refractive

index of air. The result is very close to

the theoretical value. However, the

accuracy of experiment is not high enough.

The result has an error, which is

inevitable, compared with the theoretical

value.

学霸联盟