Which of the following quantities increaes when wavelength is increased? Consider only the magnitudes

Options

A. 1.the power of a converging lens
B. 2.the focal length of a converging lens
C. 3.the power of a diverging lens
D. 4.the focal length of a diverging lens.

Answer

To solve the question "Which of the following quantities increases when wavelength is increased? Consider only the magnitudes," we will analyze the relationship between wavelength and various optical quantities.

### Step-by-Step Solution:

1. **Understanding the Relationship between Wavelength and Focal Length**:
- The focal length (f) of a lens is related to the refractive index (μ) of the material and the radii of curvature (R1 and R2) of the lens surfaces. The formula is given by:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
- The refractive index (μ) is inversely proportional to the wavelength (λ) of light. This means:
\[ \mu \propto \frac{1}{\lambda} \]
- Therefore, if the wavelength increases, the refractive index decreases, leading to an increase in the focal length:
\[ f \propto \lambda \]

2. **Analyzing Power of the Lens**:
- The power (P) of a lens is defined as the reciprocal of the focal length:
\[ P = \frac{1}{f} \]
- Since we established that the focal length increases with an increase in wavelength, it follows that the power of the lens will decrease:
\[ P \propto \frac{1}{\lambda} \]
- Thus, as the wavelength increases, the power of the lens decreases.

3. **Conclusion**:
- From the analysis above, we conclude that the quantity that increases when the wavelength is increased is the **focal length** of the lens.

### Final Answer:
The quantity that increases when the wavelength is increased is the **focal length**.

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