A student when discussing the properties of a medium ( except vaccum) writes
Velocity of light in vaccum = Velocity of light in medium
This formula is

Options

A. Dimensionally correct
B. Dimensionally incorrect
C. Numerically incorrect
D. Both `a and c`

Explanation

To solve the question regarding the statement made by the student about the velocity of light in vacuum and in a medium, we will analyze the statement step by step.

### Step 1: Understanding the Statement
The student claims that the velocity of light in vacuum is equal to the velocity of light in a medium. This can be expressed mathematically as:
\[ c = v \]
where \( c \) is the speed of light in vacuum and \( v \) is the speed of light in the medium.

### Step 2: Analyzing Dimensions
Next, we need to check the dimensions of both sides of the equation. The dimension of velocity is given by:
\[ [\text{Velocity}] = [L T^{-1}] \]
where \( L \) represents length and \( T \) represents time.

Since both \( c \) and \( v \) have the same dimensions, we can say that:
\[ [c] = [v] = [L T^{-1}] \]
This confirms that dimensionally, the equation \( c = v \) is correct.

### Step 3: Numerical Values and Refractive Index
Now, let's consider the numerical values. The refractive index \( \mu \) of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in the medium:
\[ \mu = \frac{c}{v} \]
From this equation, we can rearrange it to express the relationship between \( c \) and \( v \):
\[ c = \mu v \]
This means that the speed of light in a medium is less than that in vacuum (since \( \mu > 1 \) for any medium other than vacuum).

### Step 4: Conclusion
Thus, the original statement made by the student that \( c = v \) is incorrect in terms of numerical values. The correct relationship is:
\[ c = \mu v \]
where \( \mu \) is the refractive index of the medium. Therefore, the statement is dimensionally correct but numerically incorrect.

### Final Answer
The formula written by the student is dimensionally correct but numerically incorrect.