The time required for the light to pass through a glass slab ( refractive index=1.5) of thickness 4 mm is (c=`3xx10^(8)ms^(-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 with a refractive index of 1.5, 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 the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v):
\[ n = \frac{c}{v} \]

### Step 2: Calculate the speed of light in the glass slab
Given that the refractive index of the glass slab is 1.5, we can rearrange the formula to find the speed of light in the medium:
\[ v = \frac{c}{n} \]
Substituting the values:
- \( c = 3 \times 10^8 \, \text{m/s} \)
- \( n = 1.5 \)

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

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

### Step 4: Calculate the time taken for light to pass through the slab
The time (t) taken for light to pass through the slab can be calculated using the formula:
\[ t = \frac{\text{Thickness}}{\text{Speed in medium}} \]
Substituting the values we have:
\[ t = \frac{4 \times 10^{-3} \, \text{m}}{2 \times 10^8 \, \text{m/s}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ t = \frac{4 \times 10^{-3}}{2 \times 10^8} = 2 \times 10^{-11} \, \text{s} \]

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

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