If a very short pulse of white light were to travel through a glass plate, the colour which would emerge out of the glass plate first is

Options

A. green
B. red
C. yellow
D. violet

Answer

To solve the problem of which color of light emerges first from a glass plate when a very short pulse of white light passes through it, we can follow these steps:

### Step 1: Understand the Composition of White Light
White light is made up of multiple colors, which can be identified as red, orange, yellow, green, blue, indigo, and violet (ROYGBIV). Each color has a different wavelength.

### Step 2: Know the Refractive Index Dependency
The refractive index (μ) of a medium varies with the wavelength of light. According to Cauchy's formula, the refractive index can be expressed as:
\[ \mu = a + \frac{b}{\lambda^2} \]
where \( a \) and \( b \) are constants specific to the material, and \( \lambda \) is the wavelength of the light.

### Step 3: Analyze Wavelength and Refractive Index
From Cauchy's formula, we can infer that:
- As the wavelength increases, the refractive index decreases.
- Violet light has the shortest wavelength and thus the highest refractive index.
- Red light has the longest wavelength and thus the lowest refractive index.

### Step 4: Relate Speed of Light to Refractive Index
The speed of light in a medium is given by:
\[ v = \frac{c}{\mu} \]
where \( c \) is the speed of light in a vacuum.

### Step 5: Compare Speeds of Different Colors
Since the refractive index for red light (μ_r) is lower than that for violet light (μ_v), the speed of red light in the glass will be higher:
\[ v_r = \frac{c}{\mu_r} \]
\[ v_v = \frac{c}{\mu_v} \]
Thus, we can conclude that:
\[ v_r > v_v \]
This means red light will travel faster than violet light in the glass.

### Step 6: Conclusion
Since red light travels faster than violet light in the glass, it will emerge from the glass plate first.

### Final Answer
The color that will emerge out of the glass plate first is **Red**.

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