The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is

Options

A. `3/2`
B. `4/3`
C. `9/8`
D. `5/3`

Explanation

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

### Step 1: Understand the given data
- Power of the lens, \( P = 10 \) diopters
- Radius of curvature of each surface, \( R_1 = +10 \) cm and \( R_2 = -10 \) cm (since one surface is convex and the other is concave).

### Step 2: Convert the power to focal length
The relationship between power \( P \) and focal length \( F \) is given by:
\[ P = \frac{1}{F} \]
Thus, we can find the focal length:
\[ F = \frac{1}{P} = \frac{1}{10} = 0.1 \text{ m} = 10 \text{ cm} \]

### Step 3: Use the Lens Maker's Formula
The Lens Maker's Formula is given by:
\[ \frac{1}{F} = (n - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
Substituting the values we have:
\[ \frac{1}{10} = (n - 1) \left(\frac{1}{10} - \frac{1}{-10}\right) \]

### Step 4: Simplify the equation
Calculate the right-hand side:
\[ \frac{1}{10} - \frac{1}{-10} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \]
Now substituting this back into the equation:
\[ \frac{1}{10} = (n - 1) \left(\frac{1}{5}\right) \]

### Step 5: Solve for \( n \)
Rearranging gives:
\[ n - 1 = \frac{1}{10} \cdot 5 = \frac{1}{2} \]
Thus:
\[ n = \frac{1}{2} + 1 = \frac{3}{2} \]

### Conclusion
The refractive index of the material of the lens is:
\[ n = \frac{3}{2} \]