In optical communication system operating at 1200nm, only 2% of the source frequency is available for TV t ransmission having a bandwidth of 5 MHz. the number of TV channels that can be transmitted is

Options

A. 2 million
B. 10 million
C. 0.1 million
D. 1 million

Explanation

To solve the problem of determining the number of TV channels that can be transmitted in an optical communication system operating at a wavelength of 1200 nm, we will follow these steps:

### Step 1: Calculate the Source Frequency
The relationship between frequency (ν) and wavelength (λ) is given by the equation:
\[ \nu = \frac{c}{\lambda} \]
where:
- \( c = 3 \times 10^8 \) m/s (speed of light)
- \( \lambda = 1200 \) nm = \( 1200 \times 10^{-9} \) m

Substituting the values:
\[ \nu = \frac{3 \times 10^8}{1200 \times 10^{-9}} \]
\[ \nu = \frac{3 \times 10^8}{1.2 \times 10^{-6}} \]
\[ \nu = 2.5 \times 10^{14} \text{ Hz} \]

### Step 2: Calculate the Available Bandwidth
It is given that only 2% of the source frequency is available for TV transmission. Therefore, we calculate the available bandwidth (BW):
\[ \text{BW} = 0.02 \times \nu \]
Substituting the source frequency:
\[ \text{BW} = 0.02 \times (2.5 \times 10^{14}) \]
\[ \text{BW} = 5 \times 10^{12} \text{ Hz} \]

### Step 3: Determine the Bandwidth per TV Channel
The problem states that the bandwidth required for each TV channel is 5 MHz. We convert this to Hz:
\[ \text{Bandwidth per channel} = 5 \text{ MHz} = 5 \times 10^6 \text{ Hz} \]

### Step 4: Calculate the Number of TV Channels
The number of TV channels (N) that can be transmitted is given by the total available bandwidth divided by the bandwidth required per channel:
\[ N = \frac{\text{Total BW}}{\text{Bandwidth per channel}} \]
Substituting the values:
\[ N = \frac{5 \times 10^{12}}{5 \times 10^6} \]
\[ N = 10^6 \]

### Conclusion
The number of TV channels that can be transmitted is:
\[ N = 1,000,000 \text{ channels} \]

### Final Answer
1 million TV channels can be transmitted.

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