Chapter 36: Problem 22
Laser light of wavelength \(500.0 \mathrm{nm}\) illuminates two identical slits, producing an interference pattern on a screen \(90.0 \mathrm{~cm}\) from the slits. The bright bands are \(1.00 \mathrm{~cm}\) apart, and the third bright bands on either side of the central maximum are missing in the pattern. Find the width and the separation of the two slits.
Short Answer
Step by step solution
Understand the Problem
Use Young's Double-Slit Formula
Calculate the Slit Separation
Understand Missing Order and its Implication
Relate Missing Order to Slit Width
Conclusion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Wavelength
In the given problem, the laser light has a wavelength of 500 nm. This wavelength interacts with the slits to produce an interference pattern. Knowing the wavelength is essential, as it determines the spacing of the interference fringes on the detection screen. This pattern results from the wave nature of light experiencing constructive and destructive interference.
- The wavelength helps determine fringe position in experiments like Young's double-slit.
- Shorter wavelengths like ultraviolet light create narrower separation between fringes.
- Wavelength is crucial for calculating optical properties and understanding wave behaviors.
Fringe Separation
In the problem, the fringe separation is 1.00 cm. This is the distance between successive bright fringes that appear on a screen due to interference of light waves passing through the double slits. The separation provides insight into actual physical properties of the slits.
- The formula \( \Delta y = \frac{\lambda \cdot L}{d} \) describes fringe separation, where \( \Delta y \) is the fringe spacing.
- Increasing screen distance \( L \) increases fringe separation.
- Larger fringe separation indicates a larger distance between slits \( d \).
Destructive Interference
In the exercise, the absence of the third bright fringe indicates destructive interference. The condition is imposed by single-slit effects interacting with the double-slit pattern, causing the third fringe to "disappear." This helps us find the slit dimensions.
- Destructive interference results in missing fringes or dark areas in patterns.
- Occurs at angles where the path difference between two waves is an odd multiple of half-wavelengths.
- Can also indicate slit width characteristics when specific bright fringes are absent.
Young's Double-Slit Experiment
The experiment provides a way to measure wavelengths and explore interference effects. In the problem, it is utilized to calculate slit dimensions based on the resulting interference pattern. The appearance of bright and dark fringes is directly related to wave interference.
- The experiment helps visualize wave phenomena like interference and diffraction.
- It validates the principle of superposition of waves.
- Can be adjusted to evaluate both light and particle behaviors with modern quantum experiments.