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 given parameters, we can use the lensmaker's formula. Here’s a step-by-step solution:

### Step 1: Understand the Lensmaker's Formula
The lensmaker's formula is given by:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
where:
- \( f \) is the focal length of the lens,
- \( n \) is the refractive index of the lens,
- \( R_1 \) is the radius of curvature of the first surface,
- \( R_2 \) is the radius of curvature of the second surface.

### Step 2: Assign Values
For a biconvex lens with equal radii of curvature:
- Let \( R_1 = R \) (the radius of curvature of the first surface),
- Let \( R_2 = -R \) (the radius of curvature of the second surface, negative because it is concave).

Given:
- Refractive index \( n = 1.6 \),
- Focal length \( f = 10 \, \text{cm} \).

### Step 3: Substitute Values into the Formula
Substituting the known values into the lensmaker's formula:
\[ \frac{1}{10} = (1.6 - 1) \left( \frac{1}{R} - \frac{1}{-R} \right) \]
This simplifies to:
\[ \frac{1}{10} = 0.6 \left( \frac{1}{R} + \frac{1}{R} \right) \]
\[ \frac{1}{10} = 0.6 \left( \frac{2}{R} \right) \]

### Step 4: Simplify the Equation
Now, simplifying the equation:
\[ \frac{1}{10} = \frac{1.2}{R} \]

### Step 5: Solve for \( R \)
Cross-multiplying gives:
\[ R = 1.2 \times 10 \]
\[ R = 12 \, \text{cm} \]

### Conclusion
The radius of curvature \( R \) of the biconvex lens is \( 12 \, \text{cm} \).

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