Chapter 35: Problem 26
A plate of glass 9.00 cm long is placed in contact with a second plate and is held at a small angle with it by a metal strip 0.0800 mm thick placed under one end. The space between the plates is filled with air. The glass is illuminated from above with light having a wavelength in air of 656 nm. How many interference fringes are observed per centimeter in the reflected light?
Short Answer
Step by step solution
Understand the Problem
Identify the Interference Condition
Determine the Thickness Variation
Relate Thickness to Distance
Calculate Fringes per Unit Distance
Solve for Fringes per Centimeter
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Constructive Interference
In the context of thin film interference, like the air gap between the tilted glass plates, the condition for constructive interference is given by the formula:
- \(2d \cos \theta = m \lambda\)
This means that the path difference, which is twice the thickness of the air gap(\(2d\)), should be equal to an integer (\(m\)) multiple of the wavelength of light in the air (\(\lambda\)).
Wavelength in Air
In our exercise, the given wavelength of light in air is 656 nm (nanometers), which is a typical wavelength for visible light. When applying it to the constructive interference formula, it helps determine how many interference fringes will appear.
- The formula used is \(2d \cos \theta = m \lambda\), where \(\lambda\) is the wavelength in air.
Linear Thickness Variation
To understand how thickness varies along the plate, the thickness at any point, say distance \(x\) from the thinner edge, can be expressed linearly:
- \(d(x) = \frac{0.0800 \text{ mm}}{9.00 \text{ cm}} \cdot x\)
With this thickness variation, the path difference of the reflected light also changes, affecting constructive interference conditions across the plate. As \(x\) changes, so too does the amount of light meeting the constructive interference condition, resulting in a predictable pattern of bright and dark fringes.