The radius of curvature of the convex face of a plano convex lens is 12cm and the refractive index of the material of the lends 1.5. Then, the focal length of the lens is

Options

A. 6cm
B. 12cm
C. 18cm
D. 24cm

Explanation

To find the focal length of a plano-convex lens with a given radius of curvature and refractive index, we can use the lens maker's formula:

\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

### Step-by-step Solution:

1. **Identify the Given Values**:
- Refractive index (\(\mu\)) = 1.5
- Radius of curvature of the convex surface (\(R_1\)) = 12 cm
- Radius of curvature of the plane surface (\(R_2\)) = ∞ (infinity)

2. **Assign the Values to the Formula**:
- Since \(R_2\) is infinity, we know that \(\frac{1}{R_2} = 0\).
- Therefore, the formula simplifies to:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - 0 \right) \]

3. **Substitute the Values into the Equation**:
- Substitute \(\mu = 1.5\) and \(R_1 = 12\) cm into the equation:
\[ \frac{1}{f} = (1.5 - 1) \left( \frac{1}{12} \right) \]
- This simplifies to:
\[ \frac{1}{f} = 0.5 \times \frac{1}{12} \]

4. **Calculate \(\frac{1}{f}\)**:
- Multiply the values:
\[ \frac{1}{f} = \frac{0.5}{12} = \frac{1}{24} \]

5. **Find the Focal Length (f)**:
- Taking the reciprocal gives us the focal length:
\[ f = 24 \text{ cm} \]

### Final Answer:
The focal length of the lens is **24 cm**.

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