What is the thickness of the paper in this interference experiment?

[Matt1234]

Homework Statement

A piece of paper is placed at the end of an air wedge 4 cm long. Interference fringes appear when the light of wavelength 639 nm is reflected from the wedge. A dark fringe occurs at both the vertex of the wedge and at its paper end, and 56 bright fringes appear between. Calculate the thickness of the paper.

Homework Equations

delta X = L (lambda / 2t)

where t is the thickness of the paper
lambda = wavelength
l = length of air wedge
X = distance between fringes.

 

[Matt1234]

nevermind i got it I am stupid :(

 

[tomcue]

The interference fringes observed in this experiment are a result of the wave nature of light. When light is reflected from the air wedge, it undergoes constructive and destructive interference, resulting in the appearance of bright and dark fringes.

Using the equation provided, we can calculate the thickness of the paper by setting delta X (the distance between fringes) equal to 4 cm (the length of the air wedge) and solving for t (the thickness of the paper). We also know that the wavelength of light used is 639 nm.

Plugging these values into the equation, we get:

4 cm = (4 cm)(639 nm / 2t)

Solving for t, we get a thickness of approximately 0.0000001581 cm or 0.1581 nm for the paper.

This experiment demonstrates the principles of interference and the wave nature of light. It also serves as a practical application of these concepts in determining the thickness of a paper using interference fringes.