Assume the figure below was photographed with red light of a single wavelength Ao. The light passed through a single slit of width a and traveled distance L to the screen where the photograph was made. Consider the width of the central bright fringe, measured between the centers of the dark fringes on both sides of it. Rank from largest to smallest the widths of the central fringe in the following situations and note any cases of equality. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) (a) The experiment is performed as photographed. (b) The experiment is performed with light whose frequency is increased by 50%. (c) The experiment is performed with light whose wavelength is increased by 50%. (d) The experiment is performed with the original light and with a slit of width 2a. (e) The experiment is performed with the original light and slit and with distance 2L to the screen. Need Help? Read It
Assume the figure below was photographed with red light of a single wavelength Ao. The light passed through a single slit of width a and traveled distance L to the screen where the photograph was made. Consider the width of the central bright fringe, measured between the centers of the dark fringes on both sides of it. Rank from largest to smallest the widths of the central fringe in the following situations and note any cases of equality. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) (a) The experiment is performed as photographed. (b) The experiment is performed with light whose frequency is increased by 50%. (c) The experiment is performed with light whose wavelength is increased by 50%. (d) The experiment is performed with the original light and with a slit of width 2a. (e) The experiment is performed with the original light and slit and with distance 2L to the screen. Need Help? Read It
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![**Single-Slit Diffraction Experiment: Analysis of Central Bright Fringe Width**
**Introduction:**
The figure below illustrates a single-slit diffraction pattern generated by red light of a single wavelength, \(\lambda_0\). The light passed through a slit of width \(a\) and traveled a distance \(L\) to the screen where the photograph was taken. We aim to analyze the width of the central bright fringe, measured between the centers of the dark fringes on both sides.
**Analysis:**
Consider the width of the central bright fringe in the following experimental modifications. Rank from largest to smallest the widths of the central fringe and note any cases of equality.
**Experiments:**
(a) The experiment is performed as photographed.
(b) The experiment is performed with light whose frequency is increased by 50%.
(c) The experiment is performed with light whose wavelength is increased by 50%.
(d) The experiment is performed with the original light and with a slit of width \(2a\).
(e) The experiment is performed with the original light and slit and with distance \(2L\) to the screen.
**Diffraction Pattern:**
The image depicts the diffraction pattern observed. The central bright fringe is notably wider than the surrounding fringes, demonstrating the typical look of a single-slit diffraction pattern with red light.
**Explanation of Diffraction Pattern:**
1. **As Photographed (a):**
- The width of the central bright fringe is a reference for comparison.
2. **Increased Frequency (b):**
- Higher frequency means shorter wavelength. Since fringe width is directly proportional to wavelength, the central bright fringe will be narrower.
3. **Increased Wavelength (c):**
- Increasing the wavelength by 50% increases the fringe width by 50%, resulting in a wider central bright fringe.
4. **Wider Slit (d):**
- Doubling the slit width reduces the central bright fringe width by half, narrowing the fringe.
5. **Increased Distance (e):**
- Doubling the distance \(L\) would also double the fringe width, widening the central bright fringe.
\[ \text{Thus, the order from largest to smallest fringe width: } c > e > a > b > d \]
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**Graph:**
- The provided image is a visual representation of the single-s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feafc6826-5c88-4b32-b630-d072d1855c17%2F98d26f10-47e8-4de2-92b7-82510f1b56c2%2Fldbeynf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Single-Slit Diffraction Experiment: Analysis of Central Bright Fringe Width**
**Introduction:**
The figure below illustrates a single-slit diffraction pattern generated by red light of a single wavelength, \(\lambda_0\). The light passed through a slit of width \(a\) and traveled a distance \(L\) to the screen where the photograph was taken. We aim to analyze the width of the central bright fringe, measured between the centers of the dark fringes on both sides.
**Analysis:**
Consider the width of the central bright fringe in the following experimental modifications. Rank from largest to smallest the widths of the central fringe and note any cases of equality.
**Experiments:**
(a) The experiment is performed as photographed.
(b) The experiment is performed with light whose frequency is increased by 50%.
(c) The experiment is performed with light whose wavelength is increased by 50%.
(d) The experiment is performed with the original light and with a slit of width \(2a\).
(e) The experiment is performed with the original light and slit and with distance \(2L\) to the screen.
**Diffraction Pattern:**
The image depicts the diffraction pattern observed. The central bright fringe is notably wider than the surrounding fringes, demonstrating the typical look of a single-slit diffraction pattern with red light.
**Explanation of Diffraction Pattern:**
1. **As Photographed (a):**
- The width of the central bright fringe is a reference for comparison.
2. **Increased Frequency (b):**
- Higher frequency means shorter wavelength. Since fringe width is directly proportional to wavelength, the central bright fringe will be narrower.
3. **Increased Wavelength (c):**
- Increasing the wavelength by 50% increases the fringe width by 50%, resulting in a wider central bright fringe.
4. **Wider Slit (d):**
- Doubling the slit width reduces the central bright fringe width by half, narrowing the fringe.
5. **Increased Distance (e):**
- Doubling the distance \(L\) would also double the fringe width, widening the central bright fringe.
\[ \text{Thus, the order from largest to smallest fringe width: } c > e > a > b > d \]
**Need Further Assistance?**
Click the "Read It" button for more detailed instructions or help.
**Graph:**
- The provided image is a visual representation of the single-s
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