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

Options

A. `t/(nc)`
B. `tnc`
C. `(nt)/c`
D. `(tc)/(n)`

Answer

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

### Step 1: Understand the relationship between refractive index and velocity
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 the medium \( v \):
\[ n = \frac{c}{v} \]
From this, we can rearrange the equation to find the speed of light in the medium:
\[ v = \frac{c}{n} \]

### Step 2: Relate distance, speed, and time
The basic relationship between distance \( d \), speed \( v \), and time \( t \) is given by:
\[ d = v \cdot t \]
In this case, the distance \( d \) that light travels is the thickness of the glass plate \( t \).

### Step 3: Substitute the values into the equation
We can rearrange the equation to solve for time \( t \):
\[ t = \frac{d}{v} \]
Substituting \( d = t \) (the thickness of the glass) and \( v = \frac{c}{n} \):
\[ t = \frac{t}{\frac{c}{n}} = \frac{t \cdot n}{c} \]

### Step 4: Final expression for time
Thus, the time taken by light to travel through the thickness \( t \) of the glass plate is:
\[ t = \frac{n \cdot t}{c} \]

### Conclusion
The time taken by light to travel through the glass plate is given by:
\[ \text{Time} = \frac{n \cdot t}{c} \]