In a double-slit experiment, the slit separation is 200 times the wavelength of the light. What is the angular separation (in degrees) between two adjacent bright fringes?
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34. Wave Optics
Young's Double Slit Experiment
Problem 67b
Textbook Question
Light of wavelength 600 nm passes though two slits separated by 0.20 mm and is observed on a screen 1.0 m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0×10−16 s in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?

1
Determine the period of the light wave using the relationship between the speed of light, wavelength, and frequency. The formula for frequency is \( f = \frac{c}{\lambda} \), where \( c \) is the speed of light (\( 3.0 \times 10^8 \ \text{m/s} \)) and \( \lambda \) is the wavelength (600 nm or \( 600 \times 10^{-9} \ \text{m} \)). The period \( T \) is the reciprocal of the frequency: \( T = \frac{1}{f} \).
Substitute the given values into the formula \( f = \frac{c}{\lambda} \) to calculate the frequency of the light wave. Then, use \( T = \frac{1}{f} \) to find the period of the wave.
Compare the given time delay (\( 5.0 \times 10^{-16} \ \text{s} \)) to the period of the wave. To find the fraction of the period, divide the time delay by the period: \( \text{Fraction} = \frac{\text{Time Delay}}{T} \).
Simplify the fraction by substituting the calculated value of \( T \) from the previous step.
Interpret the result to express the fraction of the period that corresponds to the given time delay.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wavelength and Frequency
Wavelength is the distance between successive peaks of a wave, while frequency is the number of peaks that pass a point in a given time. For light, these two are related by the speed of light (c = λf), where λ is the wavelength and f is the frequency. Understanding this relationship is crucial for analyzing wave behavior, especially in interference patterns.
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Wave Period
The period of a wave is the time it takes for one complete cycle of the wave to pass a given point. It is the inverse of frequency (T = 1/f). In the context of light waves, knowing the period allows us to relate time delays, such as the one caused by the glass, to the fraction of the wave cycle that is affected.
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Phase Difference
Phase difference refers to the difference in the phase of two waves at a given point in time. It is often expressed in terms of fractions of the wavelength or cycles. In this scenario, the delay introduced by the glass results in a phase difference that can affect the interference pattern observed on the screen, making it essential to calculate the fraction of the wave period that corresponds to the time delay.
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Phase Constant of a Wave Function
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