As a ray of light entered medium P from medium Q, its velocity increased. What can be said about the refractive index of medium P as compared to that of the medium Q?

Options

A. It is lower
B. It is higher
C. It is the same
D. Nothing can be said without knowing what medium P and medium Q are.

Answer

To determine the relationship between the refractive indices of medium P and medium Q when a ray of light enters medium P from medium Q and its velocity increases, we can follow these steps:

### Step 1: Understand the relationship between velocity and refractive index
The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). Mathematically, it is given by:
\[ n = \frac{c}{v} \]

### Step 2: Identify the velocities in both mediums
Let:
- \( v \) = velocity of light in medium Q
- \( v' \) = velocity of light in medium P

According to the problem, we know that:
\[ v' > v \]
This means that the velocity of light increases when it enters medium P.

### Step 3: Write the refractive indices for both mediums
Using the definition of refractive index:
- For medium Q:
\[ n_Q = \frac{c}{v} \]
- For medium P:
\[ n_P = \frac{c}{v'} \]

### Step 4: Compare the refractive indices
To find the relationship between \( n_P \) and \( n_Q \), we can express them in terms of each other:
\[ n_Q = \frac{c}{v} \]
\[ n_P = \frac{c}{v'} \]

Since \( v' > v \), we can see that:
\[ \frac{1}{v'} < \frac{1}{v} \]
This implies:
\[ n_P < n_Q \]

### Step 5: Conclusion
Since the refractive index of medium P is less than that of medium Q, we can conclude that:
\[ n_P < n_Q \]

Thus, the refractive index of medium P is lower than that of medium Q.

### Final Answer
The refractive index of medium P is lower than that of medium Q.

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