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 1: Understand the given values
- Thickness of the slab (d) = 4 cm = 0.04 m (since we need to convert cm to meters)
- Refractive index (n) = 1.5
- Speed of light in vacuum (c) = \(3 \times 10^8\) m/s

### Step 2: Calculate the speed of light in the slab
The speed of light in a medium is given by the formula:
\[ V = \frac{c}{n} \]
Substituting the known values:
\[ V = \frac{3 \times 10^8 \text{ m/s}}{1.5} = 2 \times 10^8 \text{ m/s} \]

### Step 3: Use the formula for time
The time taken (t) to travel a distance (d) at a speed (V) is given by:
\[ t = \frac{d}{V} \]
Substituting the values we have:
\[ t = \frac{0.04 \text{ m}}{2 \times 10^8 \text{ m/s}} \]

### Step 4: Calculate the time
Now, perform the calculation:
\[ t = \frac{0.04}{2 \times 10^8} = \frac{0.04}{2} \times 10^{-8} = 0.02 \times 10^{-8} \text{ s} = 2 \times 10^{-10} \text{ s} \]

### Final Answer
The time taken by sunlight to pass through the slab is:
\[ t = 2 \times 10^{-10} \text{ seconds} \]

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