Question:
The spacing between two adjacent longitudinal modes in a plane laser resonator having separation between two mirrors, \( d = 10 \) cm, is:
The spacing between two adjacent longitudinal modes in a plane laser resonator having separation between two mirrors, \( d = 10 \) cm, is:
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Longitudinal mode spacing in a laser cavity depends on the mirror separation.
Updated On: Mar 26, 2025
- \( 1000 \) MHz
- \( 1500 \) MHz
- \( 2000 \) MHz
- \( 3000 \) MHz
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The Correct Option is C
Solution and Explanation
The longitudinal mode spacing is given by:
\[ \Delta \nu = \frac{c}{2d} \] Substituting \( c = 3 \times 10^8 \) m/s and \( d = 10 \) cm = \( 0.1 \) m:
\[ \Delta \nu = \frac{3 \times 10^8}{2 \times 0.1} = \frac{3 \times 10^8}{0.2} = 1.5 \times 10^9 \text{ Hz} = 1500 \text{ MHz} \]
\[ \Delta \nu = \frac{c}{2d} \] Substituting \( c = 3 \times 10^8 \) m/s and \( d = 10 \) cm = \( 0.1 \) m:
\[ \Delta \nu = \frac{3 \times 10^8}{2 \times 0.1} = \frac{3 \times 10^8}{0.2} = 1.5 \times 10^9 \text{ Hz} = 1500 \text{ MHz} \]
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