Which of the following quantities increase when wavelength of light is increased? Consider only the magniutude

Options

A. The power of a converging lens
B. The focal length of a converging lens
C. The power of a diverging lens
D. The focal length of a diverging lens

Explanation

To solve the question regarding which quantities increase when the wavelength of light is increased, we can follow these steps:

### Step 1: Understand the relationship between wavelength and focal length
We know that the focal length (f) of a lens is related to the refractive index (μ) and the radii of curvature (r1 and r2) of the lens using the lens maker's formula:
\[ \frac{1}{f} = \mu - 1 \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]
From this, we can conclude that focal length is inversely proportional to the refractive index.

### Step 2: Relate wavelength to refractive index
The refractive index (μ) is also related to the wavelength (λ) of light in a medium. Generally, we can say:
\[ \mu \propto \frac{1}{\lambda} \]
This means that as the wavelength increases, the refractive index decreases.

### Step 3: Determine the effect on focal length
Since the focal length is inversely proportional to the refractive index, if the refractive index decreases (as wavelength increases), the focal length must increase:
\[ f \propto \lambda \]
Thus, when the wavelength of light increases, the focal length of the lens also increases.

### Step 4: Analyze the effect on power
Power (P) of a lens is defined as:
\[ P = \frac{1}{f} \]
Since we established that the focal length increases with increasing wavelength, it follows that the power, which is inversely related to the focal length, will decrease:
\[ P \propto \frac{1}{\lambda} \]
Thus, as the wavelength increases, the power of the lens decreases.

### Step 5: Conclusion
From the analysis, we can conclude that:
- The focal length increases when the wavelength of light increases.
- The power decreases when the wavelength of light increases.

Therefore, the correct quantities that increase when the wavelength of light is increased are:
- Focal length.

### Summary of Results
- **Increase**: Focal Length
- **Decrease**: Power