The wave length of the Green light of mercury is `550 nm`. If the refractive index of the glass is `1.5`, the time period of the electrical vector in glass nearly (`C_(0)=3xx10^(8)mS^(-1)`)

Options

A. `1.8xx10^(-9)S`
B. `3.6xx10^(-15)S`
C. `9xx10^(-15)S`
D. `2.75xx10^(-15)S`

Explanation

To solve the problem, we need to find the time period of the electric vector of green light in glass given its wavelength and the refractive index of glass.

### Step-by-Step Solution:

1. **Convert Wavelength to Meters:**
The wavelength of green light is given as \( \lambda = 550 \, \text{nm} \).
\[ \lambda = 550 \times 10^{-9} \, \text{m} \]

2. **Identify the Refractive Index:**
The refractive index of glass is given as \( \mu = 1.5 \).

3. **Calculate the Speed of Light in Glass:**
The speed of light in a medium is given by the formula:
\[ C = \frac{C_0}{\mu} \]
where \( C_0 = 3 \times 10^8 \, \text{m/s} \) (the speed of light in vacuum).
Substituting the values:
\[ C = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \, \text{m/s} \]

4. **Calculate the Time Period (T):**
The time period \( T \) of the electric vector can be calculated using the formula:
\[ T = \frac{\lambda}{C} \]
Substituting the values we have:
\[ T = \frac{550 \times 10^{-9}}{2 \times 10^8} \]

5. **Perform the Calculation:**
\[ T = \frac{550 \times 10^{-9}}{2 \times 10^8} = \frac{550}{2} \times 10^{-9} \times 10^{-8} = 275 \times 10^{-17} = 2.75 \times 10^{-15} \, \text{s} \]

Thus, the time period of the electric vector in glass is approximately \( 2.75 \times 10^{-15} \, \text{s} \).