A ray of light `10^(-9)` second to cross a glass slab of refractive index 1.5. The thickness of the slab will be

Options

A. 0.1 m
B. 0.2 m
C. 0.3 m
D. 0.4 m

Answer

To find the thickness of the glass slab, we can follow these steps:

### Step 1: Understand the relationship between speed, time, and distance
The basic formula we will use is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 2: Identify the speed of light in the glass slab
The speed of light in a medium is given by:
\[ V = \frac{c}{n} \]
where:
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( n \) is the refractive index of the medium.

Given that the refractive index \( n \) of the glass slab is 1.5, we can calculate the speed of light in the glass slab.

### Step 3: Calculate the speed of light in the glass slab
Using the formula:
\[ V = \frac{3 \times 10^8 \text{ m/s}}{1.5} \]
Calculating this gives:
\[ V = 2 \times 10^8 \text{ m/s} \]

### Step 4: Use the time taken to cross the slab
The time taken to cross the slab is given as \( 10^{-9} \) seconds.

### Step 5: Calculate the thickness of the slab
Now we can use the distance formula:
\[ \text{Thickness} (t) = V \times \text{Time} \]
Substituting the values we have:
\[ t = (2 \times 10^8 \text{ m/s}) \times (10^{-9} \text{ s}) \]

### Step 6: Perform the multiplication
Calculating this gives:
\[ t = 2 \times 10^{-1} \text{ m} = 0.2 \text{ m} \]

### Final Answer
The thickness of the glass slab is \( 0.2 \) meters.

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