Light travels through a glass plate of thickness t and refractive index `mu.` If c is the speed of light in vacuum, the time taken by light to travel this thickness of glass is

Options

A. `mutc`
B. `(tc)/mu`
C. `(1)/(mut)`
D. `(mut)/c`

Answer

To solve the problem of finding the time taken by light to travel through a glass plate of thickness \( t \) and refractive index \( \mu \), we can follow these steps:

### Step 1: Understand the Refractive Index
The refractive index \( \mu \) of a medium is defined as the ratio of the speed of light in vacuum (or air) \( c \) to the speed of light in that medium \( v_m \):
\[ \mu = \frac{c}{v_m} \]
From this equation, we can express the speed of light in the medium:
\[ v_m = \frac{c}{\mu} \]

### Step 2: Use the Formula for Time
The time \( t \) taken by light to travel a distance \( d \) at speed \( v \) is given by the formula:
\[ t = \frac{d}{v} \]
In our case, the distance \( d \) is the thickness of the glass plate \( t \), and the speed \( v \) is the speed of light in the medium \( v_m \).

### Step 3: Substitute Values into the Time Formula
Substituting the values into the time formula, we have:
\[ t = \frac{t}{v_m} \]
Now, substituting \( v_m \) from Step 1:
\[ t = \frac{t}{\frac{c}{\mu}} \]

### Step 4: Simplify the Expression
This simplifies to:
\[ t = t \cdot \frac{\mu}{c} \]
Thus, the time taken by light to travel through the glass plate is:
\[ t = \frac{t \mu}{c} \]

### Final Answer
The time taken by light to travel through the glass plate of thickness \( t \) and refractive index \( \mu \) is:
\[ t = \frac{t \mu}{c} \]

---