A parallel of white light falls on a concave lens , Image of blue , red and green light are formed on other side of the lens at distance x, y and z respectively from the pole of the lens. Then :

Options

A. `xgtygtz`
B. `x gt z gt y`
C. `y gt z gt x`
D. None of these

Explanation

To solve the problem, we need to analyze the behavior of different colors of light as they pass through a concave lens. The key points to consider are the relationship between the wavelength of light, the refractive index, and the focal length of the lens.

### Step-by-Step Solution:

1. **Understanding Wavelengths of Colors**:
- The wavelengths of different colors of light vary. For visible light, the order of wavelengths from longest to shortest is:
- Red > Green > Blue
- This means that the wavelength of red light is greater than that of green light, which is in turn greater than that of blue light.

**Hint**: Remember that the wavelength of light affects how it bends when passing through a lens.

2. **Refractive Index and Wavelength**:
- The refractive index (μ) of a medium is inversely proportional to the wavelength (λ) of the light passing through it:
\[ μ \propto \frac{1}{λ} \]
- This indicates that shorter wavelengths (like blue) will have a higher refractive index compared to longer wavelengths (like red).

**Hint**: Consider how the refractive index affects the bending of light in the lens.

3. **Focal Length and Refractive Index**:
- According to the lens maker's formula, the focal length (f) of a lens is related to the refractive index:
\[ \frac{1}{f} \propto μ \]
- Since μ is inversely proportional to λ, we can conclude:
\[ f \propto λ \]
- This means that the focal length of the lens is directly proportional to the wavelength of the light.

**Hint**: Think about how the focal length changes for different colors of light.

4. **Comparing Focal Lengths**:
- Since the focal length is directly proportional to the wavelength:
- \( f_{red} > f_{green} > f_{blue} \)
- This indicates that the focal length for red light is greater than that for green light, which is greater than that for blue light.

**Hint**: Relate the focal lengths to the distances at which the images are formed.

5. **Image Distances**:
- For a concave lens, the image formed by light rays parallel to the principal axis converges at the focal point. The distances at which the images of blue, green, and red light are formed from the pole of the lens are denoted as x, y, and z respectively.
- Since the focal length for red light (y) is greater than that for green light (z), and the focal length for blue light (x) is the least:
- \( y > z > x \)

**Final Relation**:
\[ y > z > x \]

### Conclusion:
Thus, the distances at which the images of red, green, and blue light are formed from the pole of the concave lens are related as:
\[ y > z > x \]