Time taken by sunlight to pass through a window of thickness `4 mm` whose refraactive index is `(3)/(2),` is

Options

A. `2xx10^(-4) S`
B. `2xx10^(-8) S`
C. `2xx10^(-11) S`
D. `2xx10^(11) S`

Answer

To find the time taken by sunlight to pass through a window of thickness 4 mm with a refractive index of \( \frac{3}{2} \), we can follow these steps:

### Step 1: Understand the relationship between refractive index and speed of light
The refractive index (n) of a medium is defined as:
\[ n = \frac{c}{v} \]
where:
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( v \) is the speed of light in the medium.

### Step 2: Calculate the speed of light in the medium
Given that the refractive index \( n = \frac{3}{2} \), we can rearrange the formula to find \( v \):
\[ v = \frac{c}{n} = \frac{3 \times 10^8 \, \text{m/s}}{\frac{3}{2}} = 3 \times 10^8 \times \frac{2}{3} = 2 \times 10^8 \, \text{m/s} \]

### Step 3: Convert the thickness of the window to meters
The thickness of the window is given as 4 mm. To convert this to meters:
\[ \text{Thickness} = 4 \, \text{mm} = 4 \times 10^{-3} \, \text{m} \]

### Step 4: Calculate the time taken to pass through the window
Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values we have:
\[ \text{Time} = \frac{4 \times 10^{-3} \, \text{m}}{2 \times 10^8 \, \text{m/s}} = \frac{4}{2} \times 10^{-3} \times 10^{-8} = 2 \times 10^{-11} \, \text{s} \]

### Final Answer
The time taken by sunlight to pass through the window is:
\[ \text{Time} = 2 \times 10^{-11} \, \text{s} \]

---