A ray of light travels through a transparent slab with a speed of `2 xx 10^(10) cms^(-1)`. This implies that therefractive index of the slab material is

Options

A. `1.5 `
B. `0.667`
C. `2.0`
D. `6.0`

Answer

To find the refractive index of the slab material based on the speed of light traveling through it, we can follow these steps:

### Step 1: Identify the speed of light in vacuum
The speed of light in vacuum (C) is approximately:
\[ C = 3 \times 10^8 \text{ m/s} \]

### Step 2: Identify the speed of light in the slab
The speed of light in the slab (V) is given as:
\[ V = 2 \times 10^{10} \text{ cm/s} \]
To convert this to meters per second, we use the conversion factor \(1 \text{ cm} = 0.01 \text{ m}\):
\[ V = 2 \times 10^{10} \text{ cm/s} = 2 \times 10^{10} \times 0.01 \text{ m/s} = 2 \times 10^8 \text{ m/s} \]

### Step 3: Use the formula for refractive index
The refractive index (n) is defined as the ratio of the speed of light in vacuum to the speed of light in the medium:
\[ n = \frac{C}{V} \]

### Step 4: Substitute the values into the formula
Substituting the known values:
\[ n = \frac{3 \times 10^8 \text{ m/s}}{2 \times 10^8 \text{ m/s}} \]

### Step 5: Simplify the expression
Now, simplify the fraction:
\[ n = \frac{3}{2} = 1.5 \]

### Conclusion
Thus, the refractive index of the slab material is:
\[ n = 1.5 \]