The time required for the light to pass through a glass slab (refractive index=`1.5`) of thickness `4` mm is
(c=`3xx10^(8)` m `s^(-1)`, speed of light in free space)

Options

A. `10^(-11)` s
B. `2xx10^(-11)` s
C. `2xx10^(11)` s
D. `2xx10^(-5)` s

Explanation

To find the time required for light to pass through a glass slab of thickness 4 mm and refractive index 1.5, we can follow these steps:

### Step 1: Convert the thickness from mm to meters
The thickness of the glass slab is given as 4 mm. To convert this to meters:
\[ \text{Thickness} = 4 \, \text{mm} = 4 \times 10^{-3} \, \text{m} \]

### Step 2: Determine the speed of light in the glass slab
The speed of light in a medium can be calculated using the formula:
\[ v = \frac{c}{\mu} \]
where:
- \(c\) is the speed of light in vacuum (or air), which is \(3 \times 10^8 \, \text{m/s}\),
- \(\mu\) is the refractive index of the medium (1.5 for glass).

Substituting the values:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{1.5} = 2 \times 10^8 \, \text{m/s} \]

### Step 3: Calculate the time taken to pass through the slab
Using the formula for time, which is given by:
\[ t = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the thickness of the slab for distance and the speed of light in the glass for speed:
\[ t = \frac{4 \times 10^{-3} \, \text{m}}{2 \times 10^8 \, \text{m/s}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ t = \frac{4 \times 10^{-3}}{2 \times 10^8} = \frac{4}{2} \times 10^{-3} \times 10^{-8} = 2 \times 10^{-11} \, \text{s} \]

### Final Answer
The time required for light to pass through the glass slab is:
\[ t = 2 \times 10^{-11} \, \text{s} \]