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

Options

A. (a)`2xx10^(10)`
B. (b)`2xx10^(-8)`
C. (c)`2xx10^(8)`
D. (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, \( d = 4 \, \text{cm} = 4 \times 10^{-2} \, \text{m} \)
- Refractive index, \( \mu = 1.5 \)

### Step 2: Use the formula for refractive index
The refractive index \( \mu \) is given by the formula:
\[ \mu = \frac{c}{v} \]
where:
- \( c \) is the speed of light in vacuum \( (3 \times 10^8 \, \text{m/s}) \)
- \( v \) is the speed of light in the medium.

### Step 3: Calculate the speed of light in the medium
Rearranging the formula gives us:
\[ v = \frac{c}{\mu} \]
Substituting the known values:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{1.5} = 2 \times 10^8 \, \text{m/s} \]

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

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

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