A piece of glass is placed on a paper having letters of different colours. The letters of which colour will be raised maximum is

Options

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

Answer

To solve the problem of which color letter will appear raised the most when viewed through a piece of glass, we need to consider the concept of the refractive index and how it varies with different colors of light.

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
The refractive index (n) of a material is a measure of how much light slows down when it enters that material. It varies with the wavelength (λ) of light. According to Cauchy's relation, the refractive index can be expressed as:
\[ n = a + \frac{b}{\lambda^2} \]
where \( a \) and \( b \) are constants specific to the material.

2. **Wavelengths of Different Colors**:
The visible spectrum of light consists of different colors, each with a different wavelength:
- Violet (λ_v) - shortest wavelength
- Blue (λ_b)
- Green (λ_g)
- Yellow (λ_y)
- Red (λ_r) - longest wavelength

The order of wavelengths from shortest to longest is: Violet < Blue < Green < Yellow < Red.

3. **Refractive Index and Wavelength Relationship**:
Since the refractive index is inversely proportional to the wavelength, we can deduce that:
- Violet light has the highest refractive index (n_v)
- Red light has the lowest refractive index (n_r)

4. **Shift in Apparent Position**:
When light passes through a glass slab, the apparent shift in position of the letters can be calculated using the formula:
\[ \text{Shift} (S) = t \left(1 - \frac{1}{n}\right) \]
where \( t \) is the thickness of the glass slab.

5. **Comparing Shifts for Different Colors**:
Since the refractive index for violet light is the highest, the term \( \left(1 - \frac{1}{n}\right) \) will be the smallest for violet, leading to the least shift. Conversely, red light, having the lowest refractive index, will have the largest shift.

6. **Conclusion**:
Therefore, the color that will appear raised the most when viewed through the glass slab is **Red**.

### Final Answer:
The letters of **Red** color will be raised maximum when viewed through the glass.