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 determine which letter of the word "VIBGYOR" appears the least raised when viewed through a plane glass. The colors of the letters correspond to the colors of the spectrum of white light, which are arranged in the order of their wavelengths.

### Step-by-Step Solution:

1. **Understand the Concept of Apparent Depth**:
- When light passes from one medium to another (like air to glass), it bends due to refraction. This bending causes objects viewed through the medium to appear at a different depth than they actually are. The apparent depth (d') can be calculated using the formula:
\[ d' = \frac{d}{\mu} \]
where \(d\) is the real depth and \(\mu\) is the refractive index of the medium.

2. **Refractive Index and Wavelength**:
- The refractive index (\(\mu\)) of a medium is inversely proportional to the wavelength of light. This means that colors with longer wavelengths will have lower refractive indices.
- The order of colors in "VIBGYOR" from shortest to longest wavelength is:
- Violet (V) < Indigo (I) < Blue (B) < Green (G) < Yellow (Y) < Orange (O) < Red (R)

3. **Identify the Wavelengths**:
- Among the colors, red has the longest wavelength, and violet has the shortest. Therefore, the refractive index will be:
- \(\mu_{V} > \mu_{I} > \mu_{B} > \mu_{G} > \mu_{Y} > \mu_{O} > \mu_{R}\)

4. **Determine Apparent Depth for Each Color**:
- Since the apparent depth is inversely proportional to the refractive index, the color with the lowest refractive index will appear the least raised. Thus, we can conclude:
- Red (R) has the lowest refractive index, and therefore, it will have the highest apparent depth.

5. **Conclusion**:
- The letter that appears least raised when viewed through the glass is the letter 'R' (Red).

### Final Answer:
The letter which appears least raised is **R**.