A plano-convex lens is made of flint glass, its focal length is

Options

A. inversely proportional to the wavelength of light
B. longer for red than for blue
C. longer for blue than for red
D. the same for all colour

Answer

To solve the question regarding the focal length of a plano-convex lens made of flint glass and its dependence on the wavelength of light, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lens Maker's Formula**:
The lens maker's formula for a plano-convex lens is given by:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
where \( f \) is the focal length, \( n \) is the refractive index of the lens material, \( R_1 \) is the radius of curvature of the first surface, and \( R_2 \) is the radius of curvature of the second surface.

2. **Identify the Parameters for a Plano-Convex Lens**:
For a plano-convex lens:
- The first surface (convex) has a radius of curvature \( R_1 = R \).
- The second surface (plano) has an infinite radius of curvature \( R_2 = \infty \).

3. **Substituting Values into the Formula**:
Substituting the values into the lens maker's formula:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R} - 0 \right) = (n - 1) \frac{1}{R} \]
This simplifies to:
\[ f = \frac{R}{n - 1} \]

4. **Understanding the Relationship with Wavelength**:
The refractive index \( n \) of a material is dependent on the wavelength of light. Generally, the refractive index decreases with increasing wavelength (this is known as normal dispersion). Thus:
\[ n \propto \frac{1}{\lambda} \]
where \( \lambda \) is the wavelength of light.

5. **Relating Focal Length to Wavelength**:
Since \( f \) is inversely proportional to \( n \), we can conclude:
\[ f \propto \lambda \]
This means the focal length \( f \) is directly proportional to the wavelength \( \lambda \).

6. **Comparing Focal Lengths for Different Colors**:
Since red light has a longer wavelength than blue light, we can conclude:
- The focal length for red light (\( f_{red} \)) is greater than the focal length for blue light (\( f_{blue} \)):
\[ f_{red} > f_{blue} \]

7. **Conclusion**:
Therefore, the correct option is that the focal length is longer for red light than for blue light.

### Final Answer:
The focal length of the plano-convex lens made of flint glass is longer for red light than for blue light.

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