The refractive index of a liquid is 1.5. If the velocity of light in vacuum is 3.0 x 10$^8ms^{-1}$, the velocity of light in the liquid is

1. Analyze the question

We are given the refractive index ($n$) of a liquid and the speed of light in a vacuum ($c$). We need to find the speed of light in that specific liquid ($v$).

2. Explain the concept

The refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium. The formula is:

Where:

• $n$ = refractive index
• $c$ = speed of light in vacuum ($3.0 \times 10^8 \, \text{ms}^{-1}$)
• $v$ = speed of light in the medium (the liquid)

To find $v$, we rearrange the formula:

3. Show the solution

• Given: • $n = 1.5$ • $c = 3.0 \times 10^8 \, \text{ms}^{-1}$

• Calculation: $$v = \frac{3.0 \times 10^8}{1.5}$$

To simplify this, you can write $1.5$ as $\frac{3}{2}$:

4. Identify the answer

Comparing our result to the given options, the correct value is $2.0 \times 10^8 \, \text{ms}^{-1}$, which corresponds to option B.

5. Tip

When dealing with refractive index problems, always remember that the speed of light in any medium (other than a vacuum) will always be slower than the speed of light in a vacuum ($3.0 \times 10^8 \, \text{ms}^{-1}$). If your calculated answer is higher than $3.0 \times 10^8$, you have likely multiplied instead of divided!