Thickness of a Thin Paper – Air Wedge

Thickness of a Thin Paper – Air Wedge

AIM - 

To calculate the thickness of a thin paper by forming interference fringes using an air wedge arrangement.

GENERAL OBJECTIVE -

To measure the thickness of a given thin paper by air wedge method.

SPECIFIC OBJECTIVES -

1.    To form an interference pattern between two glass plates using air wedge setup.

2.    To calculate the band width of the interference pattern from the microscope readings.

3.    To measure the length of the air wedge using a scale.

4.    To determine the thickness of a given material using formula.

APPARATUS REQUIRED -

  1. Travelling microscope.
  2. Optically plane glass plates.
  3. A thin paper.
  4. Sodium Vapour lamp.
  5. Reading lens.
  6. Scale.

PREREQUISITE KNOWLEDGE-

  1. Air wedge - A wedge-shaped air film enclosed between two plane glass plates.
  2. Interference - When two light waves from different coherent sources meet together, the distribution of energy due to one wave is disturbed by the other. This modification in the distribution of light energy due to superposition of two light waves is called "Interference".
  3. Fringe width - The distance between any two consecutive bright or dark bands is called fringe width.
  4. Constructive and destructive interference - When the crests or troughs of two interfering waves meet, constructive interferences are formed. When the crest of one wave meets the trough of another wave, destructive interferences are formed.

PROCEDURE -

  1. Two optically plane glass plates are placed one over the other and tied at one end. The given paper is introduced near the other end, so that an air wedge is formed.
  2. The distance between the paper and the tied end (L) is measured using a scale.
  3. Light from a sodium vapour lamp is incident on a plane glass plate inclined at 45 Degree to the horizontal.
  4. The reflected light from the plane glass plate is incident normally on the optically plane glass plates forming the air wedge and reflected back.
  5. The reflected light from the air-wedge is viewed through the eye-piece of a microscope. The microscope is moved up and down and adjusted for clear interference fringes of alternate dark and bright.
  6. The microscope is fixed so that the vertical cross-paper coincides with the dark band (say nth band) and the reading is noted.
  7. The microscope is moved across the fringes and readings are noted when the vertical cross-paper coincides with the (n+5)th, (n+10)th….. dark bands.
  8.  The observed readings are tabulated and the fringe width (β) is calculated.
  9. The thickness of the given paper/thin-sheet is calculated using the formula.
Air wedge arrangement

Figure 1.1 Air wedge arrangement.


Figure 1.2 Fringe pattern.

LEAST COUNT FOR TRAVELLING MICROSCOPE -

  • Least Count (L.C) = Value of 1 Main Scale Division (MSD)/ Number of divisions in the vernier
  • Value of 1 MSD =          cm
  • Number of divisions in the vernier=          
  • LC=                =               cm

To determine the fringe width (𝖰)

LC =              cm *TR= MSR + (VSC x LC)

 

Order of Fringes

Microscope reading

 

Width for 2 fringes (10-2m)

 

Fringe width β

(10-2m)

MSR (10-2m)

VC

(div)

TR (10-2m)

 0

2

4

6

8

10

12

14

16

18

20

 

 

 

 

 

Mean (β) =____×10-2 m

*Note: Total Reading (TR) = Main Scale Reading (MSR) + (VSC x LC)

FORMULA -

Thickness of the given paper;
t = L𝜆/2𝛽 (m)
  • Where t= Thickness of the given paper.
  • L= Distance between the tied end and the thin paper.
  • 𝜆= Wavelength of sodium vapor light (589.3nm).
  • 𝛽= Fringe width.

OBSERVATION -

Length of the air wedge, L =___× 10-2 m

Wavelength of the sodium light 𝜆 = 589.3 × 10–9 m

Fringe width 𝛽 =___× 10-2 m


CALCULATION -

Thickness of the given paper;
t = L𝜆/2𝛽 (m)


RESULT -

The thickness of a thin paper using air wedge method (t) =............ m

APPLICATIONS -

Testing the flatness of a plane surface, measuring the thickness of a thin material.

VIVA VOCE QUESTIONS -

  1. What is monochromatic light? Give an example.
  2. What is the condition for the occurrence of interference phenomenon?
  3.  When the length of the air-wedge is increased, what happens to the fringe width?
  4. Why the glass plate used in the pathway of the light source should be inclined exactly at 45°?
  5. Bright and dark fringes are formed alternatively in interference pattern. Justify.
  6. What happens to the fringe width, if the thickness of the material is increased?
  7. Why do we get straight line fringes in an air wedge?

STIMULATING QUESTIONS -

  1. Can we use the polychromatic light instead of monochromatic light in air wedge method?
  2.  Is there any loss of energy in interference phenomenon?

Reference Books -

  1. "Introduction to Solid State Physics" by Charles Kittel: This book provides a comprehensive understanding of the physics of solids, including the principles and applications of thin films and interfaces.
  2. "Optics" by Eugene Hecht: This textbook covers the fundamentals of optics, including the behavior of light at boundaries and the concept of thin-film interference, which is relevant to understanding the air wedge experiment.
  3. "Modern Physics" by Kenneth S. Krane: This book introduces various topics in modern physics, including wave-particle duality and the behavior of light. It provides a good foundation for understanding the principles behind the air wedge experiment.
  4. "Introduction to Electrodynamics" by David J. Griffiths: This textbook covers the principles of electrodynamics, including electromagnetic waves and their interaction with matter. It can be helpful in understanding the behavior of light in the context of the air wedge experiment.
  5. "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca: This book offers a comprehensive introduction to physics, covering various topics including optics and interference. It provides a solid foundation for understanding the principles underlying the air wedge experiment.

Example: Try to calculate the Thickness of paper (t) for given data.

Order of Fringes

MSR (10-2m)

VSR

0

0.3

56

2

0.4

2

4

0.4

47

6

0.4

90

8

0.5

31

10

0.5

71

12

0.6

12

14

0.6

51

16

0.6

89

18

0.7

29

20

0.7

70












Given,

1)     L= 6.6 CM

2)     The Wavelength of Monochromatic Light Used is = 589.3nm



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