A biconvex lens of radii of curvature 20 cm has refractive index 1.56 for blue colour and 1.48 for red colour. The approximate linear spread of focus for white light is

Options

A. 3.6 cm
B. 4.2 cm
C. 3.0 cm
D. 5.0 cm

Explanation

To solve the problem of finding the approximate linear spread of focus for white light through a biconvex lens with given parameters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of curvature (R) = 20 cm
- Refractive index for blue light (μ_B) = 1.56
- Refractive index for red light (μ_R) = 1.48

2. **Use the Lensmaker's Formula:**
The focal length (f) of a biconvex lens can be calculated using the formula:
\[ \frac{1}{f} = (μ - 1) \cdot \frac{2}{R} \]
Rearranging gives:
\[ f = \frac{R}{2(μ - 1)} \]

3. **Calculate the Focal Length for Red Light:**
Substitute μ_R into the formula:
\[ f_R = \frac{20}{2(1.48 - 1)} = \frac{20}{2 \cdot 0.48} = \frac{20}{0.96} \approx 20.83 \text{ cm} \]

4. **Calculate the Focal Length for Blue Light:**
Substitute μ_B into the formula:
\[ f_B = \frac{20}{2(1.56 - 1)} = \frac{20}{2 \cdot 0.56} = \frac{20}{1.12} \approx 17.86 \text{ cm} \]

5. **Calculate the Difference in Focal Lengths:**
The linear spread of the focus for white light is given by the difference in focal lengths:
\[ \Delta f = f_R - f_B = 20.83 - 17.86 \approx 2.97 \text{ cm} \]

6. **Approximate the Linear Spread:**
Rounding off the result gives us:
\[ \Delta f \approx 3 \text{ cm} \]

### Final Answer:
The approximate linear spread of focus for white light is **3 cm**.

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