Chapter 36: Problem 8
Monochromatic electromagnetic radiation with wavelength \(\lambda\) from a distant source passes through a slit. The diffraction pattern is observed on a screen 2.50 m from the slit. If the width of the central maximum is 6.00 mm, what is the slit width \(a\) if the wavelength is (a) 500 nm (visible light); (b) 50.0 \(\mu\)m (infrared radiation); (c) 0.500 nm (x rays)?
Short Answer
Step by step solution
Understanding Diffraction Pattern
Convert Units Appropriately
Calculate Slit Width for (a) Visible Light
Calculate Slit Width for (b) Infrared Radiation
Calculate Slit Width for (c) X-Rays
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Electromagnetic Radiation
The type of electromagnetic radiation used in many physics experiments is monochromatic, meaning it has a single wavelength. For instance, visible light with a wavelength of 500 nm or infrared light at 50.0 µm are examples. Each type of radiation has unique properties due to its wavelength.
Different wavelengths interact differently with materials and affect how these waves are observed in experiments, like the one described above where a beam passes through a narrow slit to create a diffraction pattern. Understanding these interactions is crucial in fields like optics and photonics.
Wavelength
Shorter wavelengths, such as X-rays ( frac{1}{2} nm), have higher energy, while longer wavelengths like infrared (50.0 µm) are lower in energy. In optical physics, knowing the wavelength is crucial for understanding how light behaves when it meets obstacles, such as slits or lenses.
In the context of diffraction, wavelength helps determine the diffraction pattern, including the width of the central maximum observed when electromagnetic waves pass through a slit.
Single-slit Diffraction
The central band, known as the central maximum, is the brightest and widest part. The size and shape of this pattern depend on the wavelength of the light and the width of the slit.
- A wider slit results in a narrower central maximum.
- A longer wavelength leads to a wider central maximum.
Central Maximum
Its width is influenced by:
- The wavelength of the light: Longer wavelengths create wider central maxima.
- The width of the slit: Narrower slits result in wider central maxima.
- The distance to the screen: Greater distances amplify the effect on observed width.