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Experiment-167 F

DIFFRACTION HALOS

Dr. D Sudhakar Rao and Ms Chaithra G M Dept of Physics, St Aloysius College, Light House Hill, Mangalore-575 003. Karnataka, INDIA.

Email:sr23us@Yahoo.com

Abstract

Diffraction halos are observed when lycopodium power sprayed on a glass plate is

illuminated with sodium vapour lamp. The diameter of the halos is determined

and particle size is calculated.

Introduction

Diffraction halo is an optical phenomenon in which light gets diffracted from the edges of a

spherical particle. Similar to rainbow diffraction haloes are also visible in sky as a circular

ring around the Sun or the Moon. Figure-1(a) shows the diffraction halos seen around the sun

formed by the particles in the atmosphere and sun light. Figure-1(b) shows the Airys disc

formed by diffraction of light through a tiny circular hole. In the case of halos, diffraction

takes place from the edges of the tiny particle. The tiny parcel becomes opaque to the light

and its circumferential edges become transparent to light. In the case of Airys disc diffraction

takes place when light gets diffracted from the circumferential edges of the circular hole. The

tiny hole becomes transparent to light and rest of the object becomes opaque to light. Figure-

2 depicts these two phenomena.

Figure-1: (a) Diffraction halos round the Sun (b) Airys disc Picture courtesy:www.pbase.com/dominiccantin/images/432772317

Fraunhofer diffraction pattern due to a single circular aperture is characterized by a very

bright central disc called the Airy’s disc centered on the geometrical image of the source and

surrounded by concentric dark and bright circular rings of rapidly decreasing intensity [1].

The diffraction pattern of a number of irregularly distributed identical circular apertures can

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be shown to be the same source as that of a single aperture except for the fact that in this case

the intensity of the rings surrounded by Airy’s disc is greatly increased. From Babinet’s

principle it follows that the circular aperture may be equivalently replaced by a large number

of irregularly distributed identical circular, opaque objects without altering the diffraction

pattern [2, 3,4,5]. By measuring the diameter of the rings formed in both the cases, the

dimension of the particle diffracting the light in the case of halos or the size of the hole

through light is getting diffracted can be estimated.

Diffracted light form Airy’s disc

Diffracted light formhalos

Monochromatic light

Rest of the object becomesobstacles to light

Light diffractingthrough the hole

Object becomesobstacles to light

Figure-2: Diffraction of light forming Airy’s disc (left) and halos (right)

The above distribution is achieved in practice by dusting a glass plate with Lycopodium

powder, the particles of which are not only spherical but are of remarkably constant size.

When illuminated by monochromic light, the diffraction halos are observed. Calculation by

Sir George Airy show that if the first dark ring is seen in the direction θ 1, then

θ 1 = d

λ22.1 …1

Where λ is the wavelength of light

d is the diameter of the particles.

For the second and third rings when seen in the directions θ 2 and θ 3 respectively, we have

θ 2 = d

λ27.2 …2

d

λ23.3=θ3 …3

If the first, second and third bright rings are seen in the directionsθ 1, θ 2 and θ 3 respectively,

then

d

λ635.1≈θ1 ,

d

λ68.2≈θ2 , and

d

λ7.3≈θ3 …4

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By moving the glass plate to and fro, the diameter of the circular rings may be altered. To

determine the ring diameter a circularly perforated screen is used as shown in the Figure-3.

By moving glass plate containing the Lycopodium powder, the rings formed is coincided

with the perforated rings marked on the plate.

Figure-3: Complete experimental setup

Apparatus Used

Sodium vapor lamp, optical bench with uprights, metal plate with equidistance holes drilled,

glass plate (3”x2”) and Lycopodium powder.

Experimental Procedure

1. Experimental set up is shown in the Figure-3.

2. Lycopodium powder is dusted uniformly on a glass plate and fitted to upright of the

optical bench.

3. On a metal sheet, number of small holes (2mm) are drilled at definite radial distances

and fitted in front of the sodium light. Light passing through these holes fall on the

glass plate containing Lycopodium powder.

4. Diffraction halos are observed when viewed through the eye piece. The pattern looks

like a set of regularly placed rings.

5. The first dark ring in diffraction pattern is made to coincide with the first set of holes

drilled on the metal plate. Therefore

θ 1 = d

λ22.1 =

1

1

D

r

From which

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d = 1

1

D×r

λ22.1

Using this equation, diameter of the Lycopodium powder particles is calculated and

presented in Table-1.

6. Trial is repeated by coinciding the second and third rings on the metal plate are made

to coincide with the first diffraction dark ring, by moving the glass plate and

measuring the radii and distance of the glass plate from the metal plate, diameter of

the particles can be calculated.

7. Experiment is repeated for the second dark ring of the diffraction pattern also. The

results are tabulated in Table-1.

Table – 1

Order of the

ring (n)

Radius of the

ring

R(m)

Distance

between glass

plate and

metal plate

D(m)

Diameter of Lycopodium

powder

d= )m(10×λn×r

D5

For first ring

n= 1.22

0.010 0.411 2.955

0.015 0.641 3.0723

0.020 0.891 3.2029

0.025 1.092 3.1403

For second ring

n= 2.27

0.010 0.213 2.8493

0.015 0.352 3.1416

0.020 0.471 3.1503

0.025 0.565 3.0232

Experimental observations Wavelength of sodium light, λ = 589.3 nm

Results

Average diameter of the Lycopodium powder particles, d = 3.067X10-5

m

The standard sizes of Lycopodium powder vary from 2.8 x 10-5

m to 3.5x10-5

m.

References

[1] Dr Jeethendra Kumar P K, Fraunhoffer diffraction at circular aperture, LE Vol-3, No-

4, Page-284.

[2] James Mallmann , Halos, Rings, and Arcs in the Sky

[3] James A. Lock and James H. Andrews, Optical caustics in natural phenomena

[4] Roy H.Biser Modern methods for the Study of Optical Diffraction

[5] David Dutton, M Parker Givens, and Robert E. Hopkins, Some Demonstration

Experiments in Optics using a Gas Laser.