A convex lens of refractive index 1.5 is given. It also has the radius of curvature of both the surfaces as 40 cm. Using this data, calculate the power of this lens.

Options

A. 2.5 D
B. B 2D
C. 1.5 D
D. 1D

Explanation

To calculate the power of a convex lens given its refractive index and radius of curvature, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Refractive index (μ) = 1.5
- Radius of curvature of both surfaces (R1 and R2) = 40 cm

2. **Determine the Sign of the Radii:**
- For a convex lens, the radius of curvature for the first surface (R1) is positive, and for the second surface (R2), it is negative.
- Therefore, R1 = +40 cm and R2 = -40 cm.

3. **Use the Lens Maker's Formula:**
The lens maker's formula relates the focal length (f) of the lens to the refractive index and the radii of curvature:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

4. **Substitute the Values into the Formula:**
\[ \frac{1}{f} = (1.5 - 1) \left( \frac{1}{40} - \frac{1}{-40} \right) \]
\[ \frac{1}{f} = 0.5 \left( \frac{1}{40} + \frac{1}{40} \right) \]
\[ \frac{1}{f} = 0.5 \left( \frac{2}{40} \right) \]
\[ \frac{1}{f} = 0.5 \times \frac{1}{20} = \frac{1}{40} \]

5. **Calculate the Focal Length (f):**
\[ f = 40 \text{ cm} = 0.4 \text{ m} \]

6. **Calculate the Power (P) of the Lens:**
The power of a lens is given by the formula:
\[ P = \frac{1}{f} \text{ (in meters)} \]
\[ P = \frac{1}{0.4} = 2.5 \text{ diopters} \]

### Final Answer:
The power of the lens is **2.5 diopters**.

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