The diameter of the eye ball of a normal eye is about 2.5cm. The power of the eye lens varies from

Options

A. 9D to 8D
B. 40D to 32D
C. 44D to 40D
D. None of these

Explanation

To determine the power of the eye lens in a normal eye with a diameter of about 2.5 cm, we will analyze two cases: one for distant vision and one for near vision.

### Step-by-Step Solution:

**Step 1: Understand the Diameter of the Eyeball**
- The diameter of the eyeball is given as 2.5 cm, which is equivalent to 0.025 m.

**Step 2: Calculate the Power for Distant Vision**
- For distant objects, the object distance (u) is considered to be at infinity (u = ∞).
- The image distance (v) is equal to the radius of the eyeball, which is half of the diameter. Therefore, v = 0.025 m.
- We use the lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Substituting the values:
\[ \frac{1}{f} = \frac{1}{0.025} - \frac{1}{\infty} = \frac{1}{0.025} - 0 = \frac{1}{0.025} \]
\[ \frac{1}{f} = 40 \text{ m}^{-1} \]
Therefore, the focal length (f) is:
\[ f = \frac{1}{40} \text{ m} = 0.025 \text{ m} \]

**Step 3: Calculate the Power for Distant Vision**
- The power (P) of the lens is given by:
\[ P = \frac{1}{f} \text{ (in meters)} \]
Thus, substituting the focal length:
\[ P = 40 \text{ D (diopters)} \]

**Step 4: Calculate the Power for Near Vision**
- For near vision, the least distance of distinct vision (u) is taken as 25 cm or 0.25 m.
- The image distance (v) remains the same at 0.025 m.
- Using the lens formula again:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Substituting the values:
\[ \frac{1}{f} = \frac{1}{0.025} - \frac{1}{0.25} \]
\[ \frac{1}{f} = 40 - 4 = 36 \text{ m}^{-1} \]
Therefore, the focal length (f) is:
\[ f = \frac{1}{36} \text{ m} \]

**Step 5: Calculate the Power for Near Vision**
- The power (P) of the lens for near vision is:
\[ P = \frac{1}{f} = 36 \text{ D (diopters)} \]

**Step 6: Determine the Range of Power**
- The power of the eye lens varies from 40 D (for distant vision) to 44 D (for near vision).

### Final Answer:
The power of the eye lens varies from **40 D to 44 D**.

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