Light of wavelength 5000 A.falls on a plane reflecting surface. The frequency of reflected light is…

Options

A. `6 xx 10^(14)`Hz
B. ` 5 xx 10^(14)`Hz
C. `2xx10^(14)Hz`
D. `1.666xx10^(14)Hz`

Answer

To find the frequency of the reflected light when light of wavelength 5000 Angstroms falls on a plane reflecting surface, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The speed of light (v) is related to its frequency (ν) and wavelength (λ) by the equation:
\[ v = ν \cdot λ \]
Where:
- \( v \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( ν \) is the frequency in hertz (Hz),
- \( λ \) is the wavelength in meters (m).

### Step 2: Convert the wavelength from Angstroms to meters
The given wavelength is 5000 Angstroms. To convert Angstroms to meters, we use the conversion factor:
\[ 1 \, \text{Angstrom} = 10^{-10} \, \text{meters} \]
Thus,
\[ λ = 5000 \, \text{Angstroms} = 5000 \times 10^{-10} \, \text{meters} = 5 \times 10^{-7} \, \text{meters} \]

### Step 3: Substitute the values into the frequency formula
Now, we can rearrange the equation \( v = ν \cdot λ \) to solve for frequency:
\[ ν = \frac{v}{λ} \]
Substituting the values:
\[ ν = \frac{3 \times 10^8 \, \text{m/s}}{5 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate the frequency
Calculating the frequency:
\[ ν = \frac{3 \times 10^8}{5 \times 10^{-7}} = 3 \times 10^8 \times \frac{1}{5} \times 10^7 = \frac{3}{5} \times 10^{15} \]
\[ ν = 0.6 \times 10^{15} \, \text{Hz} = 6 \times 10^{14} \, \text{Hz} \]

### Conclusion
The frequency of the reflected light is:
\[ ν = 6 \times 10^{14} \, \text{Hz} \]

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