The time taken by light to cross a glass slab of thickness 4 mm and refractive index 3 is

Options

A. `8xx10^(-12)s`
B. `8xx10^(-10)s`
C. `4xx10^(-11)s`
D. `2xx10^(-11)s`

Answer

To find the time taken by light to cross a glass slab of thickness 4 mm and refractive index 3, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Thickness of the glass slab (d) = 4 mm
- Refractive index (μ) = 3

2. **Convert Thickness to Meters:**
- Since the thickness is given in millimeters, we convert it to meters:
\[ d = 4 \text{ mm} = 4 \times 10^{-3} \text{ m} \]

3. **Use the Formula for Time:**
- The time taken (t) for light to travel through a medium can be calculated using the formula:
\[ t = \frac{d}{v} \]
- Where \(v\) is the speed of light in the medium.

4. **Calculate the Speed of Light in the Medium:**
- The speed of light in a vacuum (c) is approximately \(3 \times 10^8 \text{ m/s}\).
- The speed of light in the medium (v) can be calculated using the refractive index:
\[ v = \frac{c}{\mu} \]
- Substituting the values:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{3} = 1 \times 10^8 \text{ m/s} \]

5. **Calculate the Time Taken:**
- Now, substituting the values of \(d\) and \(v\) into the time formula:
\[ t = \frac{4 \times 10^{-3} \text{ m}}{1 \times 10^8 \text{ m/s}} = 4 \times 10^{-11} \text{ s} \]

6. **Final Answer:**
- The time taken by light to cross the glass slab is:
\[ t = 4 \times 10^{-11} \text{ seconds} \]