The distance of the eye lens from the retina is x. For a normal eye, the maximum focal length of the eye lens

Options

A. `=x`
B. `ltx`
C. `gtx`
D. `=2x`

Answer

To solve the problem, we need to determine the maximum focal length of the eye lens when the distance from the eye lens to the retina is given as \( x \).

### Step-by-Step Solution:

1. **Understanding the Eye Structure**:
- The eye lens focuses light onto the retina. The distance from the eye lens to the retina is given as \( x \).

2. **Condition for Maximum Focal Length**:
- The maximum focal length of the eye lens occurs when the object is at infinity. When an object is at infinity, the rays of light coming from it are parallel to the optical axis of the lens.

3. **Image Formation**:
- For a lens, when parallel rays (from an object at infinity) pass through it, they converge at the focal point of the lens. Thus, the image of the object at infinity will be formed at the focal point of the lens.

4. **Relating Focal Length to Distance**:
- For the image to be formed on the retina, the focal length of the eye lens must equal the distance from the lens to the retina. Since this distance is given as \( x \), we can conclude that:
\[ f = x \]
where \( f \) is the focal length of the eye lens.

5. **Conclusion**:
- Therefore, the maximum focal length of the eye lens for a normal eye, when the distance to the retina is \( x \), is:
\[ \text{Maximum Focal Length} = x \]

### Final Answer:
The maximum focal length of the eye lens is \( x \).