SCHOOL NAME SCHOOL NAME SCHOOL NAME - ammhu.com fileapparatus required A Helium-Neon Leaser, A single slit , A Meter scale, A Travelling microscope and a screen (a white wall with

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www.ammhu.com A categorized blogging website and an Online Resource Centre For CBSE, RBSE, and Other State Boards — Raj Kumar Parashari, Head Science @ JPHS, Jaipur-302021

SCHOOL NAME SCHOOL NAME SCHOOL NAME

ADDRESS WITH PINCODE AND PHONE NUMBER

Submitted by Guided by

Student Name [ Teacher Name ]

XII Sc ……

Board Roll No. Designation

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INDEX

I. Certificate

II. Acknowledgement

1. Aim/ Objective

2. Apparatus Required

3. Theory

4. Experimental Demonstration of Diffraction

5. Experimental Set up & Procedure

6. Observations

7. Calculations

8. Result

9. Precautions

10. Bibliography

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CERTIFICATE

This is to certify that _______________________ student of

______ school name _______, class XII Sc __ has carried out

his work for the investigatory project entitled

_______________________________________ under my guidance

and supervision.

Signature of the Teacher

Name Of The Teacher

Designation

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ACKNOWLEDGEMENT

I __________________________________ a student of

____________________________________,______________ would like to pay

my sincere gratitude to my Physics teacher Mr./Mrs.

__________________________ for helping and guiding me throughout

the completion of the project report. I would like to thank

Mr./Mrs. _______________________ our school principal/Director

for making school such a wonderful place of learning. I also

would like to thank Mr. ______________ our lab assistant for the

timely assistant in completion of the project.

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1. AIM Determination Of Wavelength of Laser Light Beam By Observing

Diffraction Through Single Slit

2. APPARATUS REQUIRED A Helium-Neon Leaser, A single slit , A Meter scale, A Travelling

microscope and a screen (a white wall with a graph paper pasted on it

can serve as a good screen.)

3. THEORY The phenomenon of bending of light around the corners of small

obstacles or apertures and its consequent spreading into the regions of

geometrical shadow is called diffraction of light. It is prominent when

wavelength of incident light is of the order of size of aperture or obstacle.

Diffraction of light at a single slit : Consider a plane wavefront

WW' of monochromatic light incident normally on a narrow rectangular

slit AB. According to Huygens' theory, all parts of the slit AB will become

source of secondary wavelets, which all start in the same phase. These

secondary wavelets spread out in all directions and superposes to

produce diffraction pattern, which is focused by a convex lens L2 on a

screen placed in its focal plane.

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The secondary wavelets originated from the and of wavefront (A, B)

produces zero path difference or zero phase difference on reaching point

O (Point O lies at the perpendicular bisector of line joining A and B) and

hence superpose constructively to produce bright region. Same argument

for all the pair of sources such as (A1, B1), (A2, B2) and shown thus we

get central maxima at point O.

Positions of secondary minima : Let the point P be the point

where first secondary minima in located. Position of first secondary

minima could be explained provided path difference between waves

emitted from the ends of wave front .

Let us divide the wave front into two halves AC and CB then the path

difference between the wavelets from any two corresponding points of

AC and CB will be /2. These wavelets add up destructively to produce a

minimum, so does effect of all pair of sources such as (A1, C1), (A2, C2),

.........

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Thus the condition for first secondary minima is

or BP – AP =

or a sin 1 =

The condition for nth dark fringe can be written as

a sin n = n , where n = 1, 2, 3,...

Positions of secondary maxima : Let the point P be the point

where first secondary maxima is located. Position of first secondary maxima could

be explained provided path difference between waves emitted from the ends of

wave front = 3 / 2 .

Let us divide the wave front into three halves AC, CD and DB then the path

difference between the wavelets from any two corresponding points of AC and CD

will be /2. These wavelets add up destructively to produce a minimum, so does is

effect of all pair of sources such as (A1, C1), (A2, C2), ......... Thus effect of AC part of

wave front is canceled by CD part of the wave front. All the secondary wave

originated from DB part of the wave front meet at point P and superpose

constructively and we get first secondary maxima.

Thus the condition for first secondary maxima is

or BP – AP = 3 / 2

or a sin 1 = 3 / 2

The condition for nth secondary maxima can be written as

na sin ' ( 2n 1) ,2

n = 1, 2, 3, ......

The intensity of secondary maxima decreases as n increases.

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(b) Width of central maxima is equal to separation between first secondary

minima on either side of central maxima.

Thus W = 2 x1

For first secondary minima

a sin 1 =

or,

1xa

D

or, 1

Dx

a

So , 1

2 DW 2x

a

Which is the required the formula for the width of central maxima

Note:- Angular width of central maxima, It is the angle made by width of

central maxima at the centre of slit. It is given by

W 22

D a

and it does not depend upon ‘D’ i.e. distance of the screen from the slit.

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(c) The variation of intensity with phase difference in a single slit diffraction

experiment.

4. EXPERIMENTAL DEMONSTRATION OF DIFFRACTION

PATTERN

i). Procure a special electronic bulb with a single straight filament. This bulb with

single straight filament can serve as a line source for all particle purposes.

ii). Paste a thin sheet of tin foil on a glass plate & cut a thin slit by means of sharp

needle or a blade.

iii). Cover the electric lamp with an enclose made of glass (red) or transparent red

sheet which acts as a filter for transmitting only red light.

iv). Arrange the slit ‘s’ and the screen as shown in fig. (a). A convex lens '' 1L should

be placed before the line of source in such a way that the line source lies at the

principle focus of lens '' 1L . In this position convex lens forms the image of the line of

source at infinity and ray coming from the source at infinity form a parallel beam of

light. These parallel rays fall on the slit ‘s’.

v). Parallel rays of light on passing through the slit ‘s’ diverge out. These

diverging rays are focused on the screen by another lens 2L shown in fig. (a).

vi). On the screen diffraction pattern is observed. It consist of central maximum

surrounded by alternate minima and maxima of varying intensity.

vii). The geometrical image of the slit which in present case is equal to the width of

the slit (in fig. (b)).

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viii). The diffraction pattern is obtained on the screen (fig. (c).)

ix). In big (d) the variation of intensity ‘I’ with the midpoint of central maximum

have been shown.

DIFFRACTION BY A LASER BEAM

WHAT IS LASER? LASER stands for Light Amplification by Stimulated

Emission of Radiation. A laser beam has high degree of coherence among emitted

photons, so source is monochromatic and intense. It has directional properties as

well.

Observing diffraction using LASER is very simple; just allow laser beam to fall over a

single slit and observe diffraction pattern on the screen. You need to have a laser

source and a narrow slit which can be made using shaving blade and tape.

A laser beam after passing through a narrow slit produces on the screen

several spots due to diffraction (fig. 3).

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Diffraction pattern consist a central maximum at O, with a series of dark and

bright spots on either of its side called respectively as the secondary minima and

maxima. The intensity of light falls off considerably on both sides of central

maximum. The variation of intensity with a distance from the mid-point O of central

maximum is shown in (fig 4).

Let D be the distance of slit from screen, d be the width of slit and x be the half

width of central maximum. Then wavelength of light is given be relation

d x

D

5. EXPERIMENTAL SET UP & PROCEDURE: -

i). Mount the slit on a stand and place it in front of the He-Ne laser device, so that

laser beam falls on the single slit.

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ii). View the diffraction pattern on white wall situated suitably long distance

away from the slit. A graph is pasted on the wall at the place where diffraction

pattern is expected to be obtained.

iii). Adjust the height and portion of the slit in front of the laser beam so that a

good diffraction pattern with distinct maxima and minima obtained on the wall.

iv). Measure ‘x’ distance between mid-point of central maximum and mid-point of

first minimum with the help of graph paper. Measure ‘x’ on both sides of central

maximum and take the mean of two readings.

v). Measure the distance between the slit and the screen (i.e. wall) with the help

of a meter scale & thread.

vi). Measure the slit width‘d’ with travelling microscope.

vii). Take several readings by changing D & d.

6. OBSERVATIONS

Reading of

microscope at the

lower edge x1 cm

Reading of

microscope at the

lower edge x2 cm

12 xxd (cm)

Slit 1

1.

9.50 + 0.042 = 9.542

9.55 + 0.022 = 9.572

9.572 - 9.542 = 0.030

Slit 2

2.

9.45 + 0.031 = 9.481

9.50 + 0.006 = 9.506

9.506 – 9.481 = 0.025

(b) Half linear width of central maxima (x) & Wavelength of

Laser Beam

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S. No.

Slit Width d (cm)

Distance of screen from slits D (cm)

Half linear width x (cm)

Wavelength of lightxd / D

1. 0.030 cm 300 cm 1 3 2 0 65. / . cm 56 500 10. cm

2. 0.030 cm 200 cm 0 9 2 45. . / . cm 56 750 10.

3. 0.025 cm 300 cm 1 6 2 0 80. / . cm 510667.6

4. 0.025 cm 200 cm 1 1 2 0 55. / . cm 56 875 10.

7. CALCULATION S

x.d / D

5

1

0 65 0 036 500 10

300

. .. cm

, 5

2

0 45 0 036 750 10

200

. .. cm

5

3

0 80 0 0256 667 10

300

. .. cm

, 5

4

0 55 0 0256 875 10

200

. .. cm

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1 2 3 4

4mean

A

m

cm

6698

106698

10698.6

10

5

8. RESULT

The mean wavelength of light source is 6698 A°.

9. PRECAUTIONS

1. The slit should be sufficiently narrow to obtain a good diffraction pattern.

2. Slit width should be measured with a travelling microscope after finding its least count ( usually it is 0.01mm).

3. x should be measured accurately on a graph paper by counting its square properly.

4. Don’t look into the laser beam directly. It can damage your eye.

10. BIBLIOGRAPHY

1. CBSE Compendium

2. NCERT

3. University Physics.

4. Concepts Of Physics by by H.C. Verma

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1. Note: — You need to have your own observation graph

sheets. Values for half linear width and slit width of different

students can be different

Note: — Hand written Investigatory Project Report should be

submitted. Work should be neat and clean. Avoid unnecessary

fancy decoration of the project report.

Note: — Learn theory, working and related viva for board

practical examination.

Wish you all the best.

Raj Kumar Parashari

Head Science , JPHS, Jaipur

Documents

SCHOOL NAME SCHOOL NAME SCHOOL NAME - ammhu.com fileapparatus required A Helium-Neon Leaser, A single slit , A Meter scale, A Travelling microscope and a screen (a white wall with