14 Monochromatic visible light of frequency 4.26x10 Hz falls on a single slit with aperture width 6.66 µm and creates a diffraction pattern on a screen 3.16 m away. Find the angular width of the central maximum, in degrees.
14 Monochromatic visible light of frequency 4.26x10 Hz falls on a single slit with aperture width 6.66 µm and creates a diffraction pattern on a screen 3.16 m away. Find the angular width of the central maximum, in degrees.
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![**Problem Statement: Diffraction of Light Through a Single Slit**
Monochromatic visible light of frequency \(4.26 \times 10^{14}\) Hz falls on a single slit with an aperture width of 6.66 µm and creates a diffraction pattern on a screen 3.16 m away. Find the angular width of the central maximum, in degrees.
**Concept Explanation:**
When light passes through a single slit, it diffracts and creates a pattern of bright and dark regions on a screen. The central maximum is the brightest part of the diffraction pattern. The angular width of the central maximum is an important parameter that can be calculated using the formula:
\[
\theta = \frac{\lambda}{a}
\]
Where:
- \(\theta\) is the angle of the first minimum on either side (thus, twice this angle gives the total angular width of the central maximum).
- \(\lambda\) is the wavelength of the light.
- \(a\) is the width of the slit.
The wavelength (\(\lambda\)) can be found from the frequency (\(f\)) using the speed of light (\(c\)):
\[
\lambda = \frac{c}{f}
\]
Where \(c = 3.00 \times 10^8 \, \text{m/s}\).
**Explanation for the Diagram (if applicable):**
If there were diagrams, they would typically show:
- A side view of the experimental setup, including the light source, slit, and screen.
- The resulting diffraction pattern on the screen.
- Labeled angles to illustrate the angular width of the central maximum.
Understanding these principles aids in understanding how light behaves in various conditions, revealing fundamental properties of wave behavior.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cf2ccab-90b1-41b4-a2b4-8d525578ce02%2F6d4b1a84-e41d-4aa9-9b26-93776484cbeb%2Fh272ml9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Diffraction of Light Through a Single Slit**
Monochromatic visible light of frequency \(4.26 \times 10^{14}\) Hz falls on a single slit with an aperture width of 6.66 µm and creates a diffraction pattern on a screen 3.16 m away. Find the angular width of the central maximum, in degrees.
**Concept Explanation:**
When light passes through a single slit, it diffracts and creates a pattern of bright and dark regions on a screen. The central maximum is the brightest part of the diffraction pattern. The angular width of the central maximum is an important parameter that can be calculated using the formula:
\[
\theta = \frac{\lambda}{a}
\]
Where:
- \(\theta\) is the angle of the first minimum on either side (thus, twice this angle gives the total angular width of the central maximum).
- \(\lambda\) is the wavelength of the light.
- \(a\) is the width of the slit.
The wavelength (\(\lambda\)) can be found from the frequency (\(f\)) using the speed of light (\(c\)):
\[
\lambda = \frac{c}{f}
\]
Where \(c = 3.00 \times 10^8 \, \text{m/s}\).
**Explanation for the Diagram (if applicable):**
If there were diagrams, they would typically show:
- A side view of the experimental setup, including the light source, slit, and screen.
- The resulting diffraction pattern on the screen.
- Labeled angles to illustrate the angular width of the central maximum.
Understanding these principles aids in understanding how light behaves in various conditions, revealing fundamental properties of wave behavior.
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