A ray of light passes normally through a slab `(mu=1.5)` of thickness t. If the speed of light in vacuum be C, then time taken by the ray to go across the slab will be

Options

A. `t/C`
B. `(3g)/(2C)`
C. `(2t)/(3C)`
D. `(4t)/(9C)`

Answer

To solve the problem of finding the time taken by a ray of light to pass through a slab of thickness \( t \) and refractive index \( \mu = 1.5 \), we can follow these steps:

### Step 1: Understand the relationship between refractive index and speed of light
The refractive index \( \mu \) of a medium is defined as the ratio of the speed of light in vacuum \( c \) to the speed of light in the medium \( v \):
\[ \mu = \frac{c}{v} \]
From this, we can express the speed of light in the medium as:
\[ v = \frac{c}{\mu} \]

### Step 2: Substitute the given value of refractive index
Given that \( \mu = 1.5 \), we can substitute this value into the equation:
\[ v = \frac{c}{1.5} = \frac{c}{\frac{3}{2}} = \frac{2c}{3} \]

### Step 3: Calculate the time taken to cross the slab
The time taken \( t \) to travel a distance \( d \) at speed \( v \) is given by the formula:
\[ t = \frac{d}{v} \]
In this case, the distance \( d \) is equal to the thickness of the slab \( t \):
\[ t = \frac{t}{v} \]
Substituting \( v = \frac{2c}{3} \) into the equation:
\[ t = \frac{t}{\frac{2c}{3}} = t \cdot \frac{3}{2c} = \frac{3t}{2c} \]

### Final Answer
Thus, the time taken by the ray to go across the slab is:
\[ \frac{3t}{2c} \]

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