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: Convert thickness to meters
The thickness of the window is given as 4 mm. We need to convert this to meters for consistency in units.

\[ \text{Thickness} = 4 \, \text{mm} = 4 \times 10^{-3} \, \text{m} \]

### Step 2: Determine the speed of light in glass
The speed of light in a medium can be calculated using the formula:

\[ v_g = \frac{c}{\mu} \]

Where:
- \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \)
- \( \mu \) is the refractive index of the medium, which is \( \frac{3}{2} \) in this case.

Substituting the values:

\[ v_g = \frac{3 \times 10^8}{\frac{3}{2}} = 3 \times 10^8 \times \frac{2}{3} = 2 \times 10^8 \, \text{m/s} \]

### Step 3: Calculate the time taken to pass through the window
The time taken \( t \) to pass through the window can be calculated using the formula:

\[ t = \frac{\text{Thickness}}{v_g} \]

Substituting the values we have:

\[ t = \frac{4 \times 10^{-3}}{2 \times 10^8} \]

### Step 4: Simplify the expression
Now, we simplify the expression:

\[ t = \frac{4}{2} \times 10^{-3} \times 10^{-8} = 2 \times 10^{-11} \, \text{s} \]

### Final Result
The time taken by sunlight to pass through the window is:

\[ t = 2 \times 10^{-11} \, \text{s} \]

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