newton rings

Interference in a Thin Film: Newton’s rings

Purpose

The purpose of this experiment was to show how light interference works in a thin film

Part 1: Thin wedge consecutive lines of fringes

Part 2: Newton’s Rings circles of fringes


Theory

Index of refraction glass n = 1.5 air n = 1.0

When nA > nB

rays reflecting from the side where n=nA reflect the same

phase rays reflecting from the side

where n=nB experience a

phase reversal


Theory

A phase reversal is equivalent to shifting the ray by half a wavelength

Diagram from Physics 294 Laboratory Manual, page 17-1


Theory

When waves interfere constructively:


Theory

When waves interfere destructively:


Theory

When waves interfere destructively:


Theory Part 1



Theory Part 1

Two glass plates at an angle cause the space between them t to increase with x t = /2 = x tan

Where t is the distance between the two pieces of

glass is the wavelength of the light x is the distance between consecutive fringes is the angle between the glass

tan = t / x Since is constant, t / x should be constant Implies fringes happen at regular intervals


Theory Part 2


Theory Part 2


Theory Part 2


Theory Part 2

Diagrams from Physics 294 Laboratory Manual, page 17-3


Theory Part 2

rm2 = xm

2/4 + 2 = mR Where

rm is the actual radius of the mth fringe

xm is the measured diameter is the perpendicular offset from the center of

the ring m is the order of the ring

m=0 for the bulls eye m=1, 2, 3, … for each consecutive ring

is the wavelength of the light R is the curvature radius of the plano-convex lens


Apparatus


Apparatus



Procedure


Procedure Part 1

The distance from an arbitrary (m=0) fringe to 20 consecutive dark fringes was measured

The difference between each fringe was calculated x = xn - xn-1

From x we can calculate /2 = x tan


Procedure Part 2

Position the microscope over the center of the bulls eye

Measure xL and xR to get xm for 10 rings xm = |xL - xR|

Plot xm2 versus m to find R and 2

xm2/4 + 2 = mR

xm2 = mR/4 - 2/4

y = mx + b


Analysis


Analysis Part 1

Error for x x = (x)2 + (x)2

x = 2(x)2 x = 2(0.004 cm)2

x = 0.006 cm

m Xm (cm) error Xm (cm) difference Xm (cm) error difference (cm)0 11.883 0.0041 11.941 0.004 0.058 0.0062 11.990 0.004 0.049 0.0063 12.040 0.004 0.050 0.0064 12.090 0.004 0.050 0.0065 12.141 0.004 0.051 0.0066 12.190 0.004 0.049 0.0067 12.233 0.004 0.043 0.0068 12.290 0.004 0.057 0.0069 12.332 0.004 0.042 0.00610 12.380 0.004 0.048 0.00611 12.432 0.004 0.052 0.00612 12.486 0.004 0.054 0.00613 12.530 0.004 0.044 0.00614 12.580 0.004 0.050 0.00615 12.632 0.004 0.052 0.00616 12.684 0.004 0.052 0.00617 12.734 0.004 0.050 0.00618 12.786 0.004 0.052 0.00619 12.838 0.004 0.052 0.00620 12.888 0.004 0.050 0.006


Analysis Part 1

Average x = 0.050 Excel “=AVERAGE(x)”

Standard Deviation x = 0.004 Excel “=STDEV(x)”


Analysis Part 1

t = /2 = x tan /2 = x tan

for sodium light is 589.3 nm = 5.893*10-7m x average was 0.050 cm = 5.0 * 10-4m

Solve for (5.893*10-7m)/2 = (5.0 * 10-4m ) tan = 3.4 * 10-2 degrees


Analysis Part 1

For small angles (tan) (tan) = (/2) / x

(tan) = (5.893*10-7m )/2 / (6*10-5 m) (tan) = .004

= 0.034 +/- .004 degrees


Analysis Part 2


Analysis Part 2

xm2 = xm

2 * (xm/xm)2 + (xm/xm)2

xm2 = xm

2 * 2(xm/xm)2

x12 = (0.062 cm) * 2(0.006/0.248)2

x12 = 0.002

m xr (cm) xl (cm) xm (cm) error xm (cm) xm 2̂ (cm) error xm 2̂ (cm)0 11.9001 11.770 12.018 0.248 0.006 0.062 0.0022 11.721 12.064 0.343 0.006 0.118 0.0033 11.678 12.092 0.414 0.006 0.171 0.0044 11.650 12.124 0.474 0.006 0.225 0.0045 11.618 12.152 0.534 0.006 0.285 0.0056 11.594 12.180 0.586 0.006 0.343 0.0057 11.576 12.202 0.626 0.006 0.392 0.0058 11.550 12.226 0.676 0.006 0.457 0.0069 11.530 12.246 0.716 0.006 0.513 0.00610 11.518 12.260 0.742 0.006 0.551 0.006


Analysis Part 2Xm^2 versus m

y = 0.0555x + 0.0064

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0 2 4 6 8 10 12

m

Xm

^2 (

cm

^2)


Used Excel’s LINEST() function to calculate slope and intercept

Slope = 0.0555 +/- 0.0006 Intercept = 0.006 +/- 0.004

0.0555 0.0060.0006 0.004


Analysis Part 2

xm2 = mR/4 - 2/4

y = 0.0555x + 0.0064 y = mx + b To find 2

- 2/4 = 0.006 2 = -0.024 cm2

2/4 = 0.004 2 = 0.02

2 = -0.02 +/- 0.02 cm2


Analysis Part 2

xm2 = mR/4 - 2/4

y = 0.0555x + 0.0064 y = mx + b To find R

mR/4 = 0.0555x where x = m = 589.3 nm = 5.893 * 10-5 cm

(5.893 * 10-5 cm)R/4 = 0.0555 R=3.767 * 103 cm


Analysis Part 2

R/4 = 0.0006 R = 0.0006 * 4 /

R = 0.0006 * 4 / 5.893 * 10-5 cm R = 40 cm

R = 3.77 * 103 +/- 0.04 * 103 cm


Conclusion

We were able to see how rays of light could interfere causing fringes

Dark fringes: destructive interference Bring fringes: constructive interference Interference explains colours in a thin film


Conclusion

Measured distance between fringes Able to calculate the thin film’s properties In Part 1 we were able to calculate

= 0.034 +/- .004 degrees In Part 2 we found

2 = -0.02 +/- 0.02 cm2

R = 3.77 * 103 +/- 0.04 * 103 cm


Conclusion

Errors Error in positioning the travelling microscope over

the same place for each fringe Error in taking measurements from the

micrometer scale Error would arise in Part 1 if the fringes were not

aligned perpendicular to the direction of the travelling microscope


Conclusion

Experiment could be improved by using a travelling light sensor instead of a

microscope


Questions?

Additional pictures at www.goldenratio.ca

Date post:	03-Jan-2016
Category:	Documents
Upload:	kantilalk
View:	215 times
Download:	14 times

newton rings

Documents