The time taken by a ray of light to travel through a glass slab of thickness 2 cm and refractive index 1.5 will be

Options

A. `10^(-8) s
B. `10 ^(-10) s`
C. `2 xx 10^(-8) s`
D. `10^(-12) s`

Explanation

To find the time taken by a ray of light to travel through a glass slab of thickness 2 cm and refractive index 1.5, we can follow these steps:

### Step 1: Convert the thickness from centimeters to meters
The thickness of the glass slab is given as 2 cm. To convert this to meters:
\[ \text{Thickness} = 2 \text{ cm} = 2 \times 10^{-2} \text{ m} \]

### Step 2: Use the refractive index to find the speed of light in the glass
The refractive index (μ) is defined as:
\[ \mu = \frac{c}{v} \]
where:
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( v \) is the speed of light in the medium (glass in this case).

Rearranging the formula to find \( v \):
\[ v = \frac{c}{\mu} \]
Substituting the values:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.5} = 2 \times 10^8 \text{ m/s} \]

### Step 3: Calculate the time taken to travel through the glass slab
The time taken (T) can be calculated using the formula:
\[ T = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is the thickness of the glass slab, and the speed is the speed of light in the glass:
\[ T = \frac{2 \times 10^{-2} \text{ m}}{2 \times 10^8 \text{ m/s}} \]

### Step 4: Simplify the expression
\[ T = \frac{2 \times 10^{-2}}{2 \times 10^8} = \frac{1}{10^8} = 10^{-10} \text{ seconds} \]

### Final Answer
The time taken by the ray of light to travel through the glass slab is:
\[ T = 10^{-10} \text{ seconds} \]

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