Air wedge interference pattern after being filled with water

In summary, the conversation discusses the effect of filling an air wedge with water on the interference pattern produced. The answer given in the book states that the fringe spacing will increase, but the reasoning presented leads to the conclusion that it will actually decrease. This is due to the higher refractive index of water, which reduces the distance needed for the optical path length to increase by a wavelength. It is possible that the book is incorrect in this matter.
  • #1
Andrew Tom
14
0
Homework Statement
Air wedge interference pattern after being filled with water
Relevant Equations
##x=\frac{\lambda}{2\tan \theta}##
An air wedge is illuminated with light and an interference pattern is produced. What will happen to the interference pattern when the air wedge is filled with water?

The answer given at the back of the book is that the fringe spacing of the interference pattern will increase, however my reasoning is leading me to the conclusion that it will decrease.

The derivation for fringe spacing given in the book for an air wedge shows that it is ##\frac{\lambda}{2\tan \theta}## where ##\theta## is the wedge angle. When I re-derived the formula using the same reasoning but for water with refractive index n I got the fringe spacing ##\frac{\lambda}{2n\tan\theta}##. So the fringe spacing will decrease because n>1 for water.
 
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  • #2
Andrew Tom said:
the interference pattern will increase
Are those the exact words? I don't know what that means.
 
  • #3
haruspex said:
Are those the exact words? I don't know what that means.
Sorry it says the fringe spacing will increase.
 
  • #4
Andrew Tom said:
Sorry it says the fringe spacing will increase.
I agree with you. A higher refractive index would mean you don't need to go so far along the wedge for the optical path length to increase by a wavelength.
 
  • #5
haruspex said:
I agree with you. A higher refractive index would mean you don't need to go so far along the wedge for the optical path length to increase by a wavelength.
So is the book wrong?
 
  • #6
Andrew Tom said:
So is the book wrong?
I would say so. Others may chip in.
 

Related to Air wedge interference pattern after being filled with water

1. What is an air wedge interference pattern?

An air wedge interference pattern is a phenomenon that occurs when a thin layer of air is trapped between two surfaces, causing light waves to interfere with each other and create a pattern of bright and dark fringes.

2. How does filling the air wedge with water affect the interference pattern?

Filling the air wedge with water changes the thickness of the medium between the two surfaces, altering the path length of the light waves and causing a shift in the interference pattern. This can result in a change in the number and position of the fringes.

3. What factors can affect the appearance of the interference pattern?

The appearance of the interference pattern can be affected by the thickness of the air wedge, the wavelength of the light source, and the refractive index of the medium between the surfaces (air or water).

4. How can the air wedge interference pattern be used in scientific research?

The air wedge interference pattern can be used to study the properties of light, such as wavelength and refraction, and to measure the refractive index of different materials. It can also be used in interferometry techniques for precise measurements in fields such as astronomy and engineering.

5. Can the air wedge interference pattern be observed in everyday life?

Yes, the air wedge interference pattern can be observed in everyday life in various forms, such as in soap bubbles, oil slicks on water, and the colors seen on the surface of a CD or DVD. It is also the principle behind the operation of thin-film interference in anti-reflective coatings on glasses and camera lenses.

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