A biconvex lens with equal radii curvature has refractive index 1.6 and focal length 10 cm. Its radius of curvature will be:

Options

A. 20 cm
B. 16 cm
C. 10 cm
D. 12 cm

Answer

To find the radius of curvature of a biconvex lens with equal radii of curvature, we can use the lens maker's formula, which relates the focal length (F), radius of curvature (R), and refractive index (μ) of the lens material. The formula is given by:

\[ F = \frac{R}{2(\mu - 1)} \]

### Step-by-step Solution:

1. **Identify the given values:**
- Refractive index (μ) = 1.6
- Focal length (F) = 10 cm

2. **Substitute the values into the lens maker's formula:**
\[ F = \frac{R}{2(\mu - 1)} \]
Plugging in the values we have:
\[ 10 = \frac{R}{2(1.6 - 1)} \]

3. **Calculate (μ - 1):**
\[ \mu - 1 = 1.6 - 1 = 0.6 \]

4. **Substitute (μ - 1) back into the equation:**
\[ 10 = \frac{R}{2 \times 0.6} \]
This simplifies to:
\[ 10 = \frac{R}{1.2} \]

5. **Rearranging to solve for R:**
Multiply both sides by 1.2:
\[ R = 10 \times 1.2 \]

6. **Calculate R:**
\[ R = 12 \text{ cm} \]

### Final Answer:
The radius of curvature (R) of the lens is **12 cm**.

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