Time taken by the sunlight to pass thought a slab of 4 cm and reflective index 1.5 is……….. S.

Options

A. `2xx10^(10)`
B. `2xx10^(-8)`
C. `2xx10^(8)`
D. `2xx10^(-10)`

Answer

To solve the problem of finding the time taken by sunlight to pass through a slab of thickness 4 cm with a refractive index of 1.5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Thickness of the slab (d) = 4 cm = 0.04 m (convert cm to meters for consistency in units)
- Refractive index (μ) = 1.5

2. **Calculate the Speed of Light in the Medium:**
- The speed of light in vacuum (c) = \(3 \times 10^8\) m/s.
- The speed of light in the medium (v) can be calculated using the formula:
\[ v = \frac{c}{\mu} \]
- Substituting the values:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.5} = 2 \times 10^8 \text{ m/s} \]

3. **Use the Formula for Time:**
- The formula relating distance, speed, and time is:
\[ d = v \times t \]
- Rearranging for time (t):
\[ t = \frac{d}{v} \]

4. **Substituting the Values:**
- Now substitute the values of d and v:
\[ t = \frac{0.04 \text{ m}}{2 \times 10^8 \text{ m/s}} \]

5. **Calculating Time:**
- Performing the calculation:
\[ t = \frac{0.04}{2 \times 10^8} = \frac{4 \times 10^{-2}}{2 \times 10^8} = 2 \times 10^{-10} \text{ seconds} \]

6. **Final Answer:**
- The time taken by the sunlight to pass through the slab is \(2 \times 10^{-10}\) seconds.