A plane glass is kept over a coloured word 'VIBGYOR', where colour of letters as same as the colours in white light start by fetter, the letter which appears least raised is

Options

A. R
B. Y
C. O
D. V

Answer

To solve the problem, we need to understand the concept of apparent depth and how it relates to the colors of light. The colored word 'VIBGYOR' corresponds to the colors of the visible spectrum, with 'V' for violet, 'I' for indigo, 'B' for blue, 'G' for green, 'Y' for yellow, 'O' for orange, and 'R' for red.

### Step-by-Step Solution:

1. **Understanding Apparent Depth**:
When light passes from one medium to another (in this case, from glass to air), it bends due to refraction. The apparent depth of an object viewed through a medium is given by the formula:
\[ \text{Apparent Depth} = \frac{\text{Real Depth}}{\mu} \]
where \( \mu \) is the refractive index of the medium.

2. **Refractive Index Values**:
- The refractive index of glass (\( \mu \)) is greater than 1.
- The refractive index of air is approximately 1.

3. **Relating Wavelength to Apparent Depth**:
The height of the image (apparent height) is inversely proportional to the refractive index. Therefore, the apparent height of the image of each color can be expressed as:
\[ h_i \propto \frac{1}{\mu} \]
Since the refractive index is greater for shorter wavelengths (like violet) and lower for longer wavelengths (like red), the apparent height of the image will vary with color.

4. **Identifying Color Wavelengths**:
The order of colors in the visible spectrum from longest wavelength to shortest is:
- Red (longest wavelength)
- Orange
- Yellow
- Green
- Blue
- Indigo
- Violet (shortest wavelength)

5. **Determining Which Color Appears Least Raised**:
Since the apparent height is inversely proportional to the refractive index, colors with longer wavelengths (like red) will appear less raised compared to those with shorter wavelengths (like violet). Therefore, the red color will appear the least raised when viewed through the glass.

6. **Conclusion**:
The letter that appears least raised when viewed through the plane glass is the letter 'R' for red.

### Final Answer:
The letter which appears least raised is 'R' (Red).

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