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Two monochromatic sources, L1 and L2 emit light at 600 nm and 700 nm respectively. If their frequency band width are 10-1 and 10-3 GHz respectively, then ratio of line width L1 and L2 is approximately___________
Correct answer is '75'. Can you explain this answer?
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Given information:
- Two monochromatic sources, L1 and L2, emit light at 600 nm and 700 nm respectively.
- The frequency bandwidth of L1 is 10-1 GHz.
- The frequency bandwidth of L2 is 10-3 GHz.
To find:
The ratio of the line width of L1 and L2.
Explanation:
The line width of a source is a measure of the range of frequencies present in its emission spectrum. It is a measure of the spread of frequencies around the central frequency.
Step 1: Calculate the line width of L1:
The frequency bandwidth of L1 is 10-1 GHz.
We know that the speed of light (c) is given by c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.
Given:
λ1 = 600 nm = 600 × 10-9 m
ν1 = ?
c = 3 × 108 m/s
We can rearrange the equation c = λν to solve for ν:
ν1 = c / λ1 = (3 × 108 m/s) / (600 × 10-9 m) = 5 × 1014 Hz
The line width of L1 is 10-1 GHz, which is equivalent to 10-4 Hz.
Step 2: Calculate the line width of L2:
The frequency bandwidth of L2 is 10-3 GHz.
Given:
λ2 = 700 nm = 700 × 10-9 m
ν2 = ?
Using the same equation c = λν and rearranging it for ν:
ν2 = c / λ2 = (3 × 108 m/s) / (700 × 10-9 m) = 4.29 × 1014 Hz
The line width of L2 is 10-3 GHz, which is equivalent to 10-6 Hz.
Step 3: Calculate the ratio of line widths:
Ratio of line widths = (line width of L1) / (line width of L2)
= (10-4 Hz) / (10-6 Hz) = 102
Therefore, the ratio of the line widths of L1 and L2 is 100.
Answer:
The ratio of the line width of L1 and L2 is approximately 100.
- Two monochromatic sources, L1 and L2, emit light at 600 nm and 700 nm respectively.
- The frequency bandwidth of L1 is 10-1 GHz.
- The frequency bandwidth of L2 is 10-3 GHz.
To find:
The ratio of the line width of L1 and L2.
Explanation:
The line width of a source is a measure of the range of frequencies present in its emission spectrum. It is a measure of the spread of frequencies around the central frequency.
Step 1: Calculate the line width of L1:
The frequency bandwidth of L1 is 10-1 GHz.
We know that the speed of light (c) is given by c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.
Given:
λ1 = 600 nm = 600 × 10-9 m
ν1 = ?
c = 3 × 108 m/s
We can rearrange the equation c = λν to solve for ν:
ν1 = c / λ1 = (3 × 108 m/s) / (600 × 10-9 m) = 5 × 1014 Hz
The line width of L1 is 10-1 GHz, which is equivalent to 10-4 Hz.
Step 2: Calculate the line width of L2:
The frequency bandwidth of L2 is 10-3 GHz.
Given:
λ2 = 700 nm = 700 × 10-9 m
ν2 = ?
Using the same equation c = λν and rearranging it for ν:
ν2 = c / λ2 = (3 × 108 m/s) / (700 × 10-9 m) = 4.29 × 1014 Hz
The line width of L2 is 10-3 GHz, which is equivalent to 10-6 Hz.
Step 3: Calculate the ratio of line widths:
Ratio of line widths = (line width of L1) / (line width of L2)
= (10-4 Hz) / (10-6 Hz) = 102
Therefore, the ratio of the line widths of L1 and L2 is 100.
Answer:
The ratio of the line width of L1 and L2 is approximately 100.
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Two monochromatic sources, L1and L2 emit light at 600 nm and 700 nm respectively. If their frequency band width are 10-1 and 10-3 GHz respectively, then ratio of line width L1and L2is approximately___________Correct answer is '75'. Can you explain this answer?
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