When monochromatic red light is used instead of blue light in a convex lens, its focal length will :-

Options

A. increase
B. decrease
C. remain same
D. does not depend on colour of light

Explanation

To solve the question regarding the effect of using monochromatic red light instead of blue light on the focal length of a convex lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The focal length (f) of a lens is related to the refractive index (n) of the lens material and the radii of curvature (R1 and R2) of the lens surfaces. The lens maker's formula is given by:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

2. **Refractive Index and Wavelength**: The refractive index of a material changes with the wavelength of light. Generally, the refractive index (n) is inversely proportional to the wavelength (λ) of the light:
\[ n \propto \frac{1}{\lambda} \]
This means that as the wavelength increases, the refractive index decreases.

3. **Comparison of Wavelengths**: The wavelength of red light is longer than that of blue light. Therefore, we can denote:
\[ \lambda_{red} > \lambda_{blue} \]
Consequently, this implies:
\[ n_{red} < n_{blue} \]

4. **Effect on Focal Length**: Since the focal length is inversely proportional to the refractive index, we can conclude:
\[ f \propto \lambda \]
Thus, if the wavelength increases (from blue to red), the focal length will also increase. Therefore, we can say:
\[ f_{red} > f_{blue} \]

5. **Final Conclusion**: When monochromatic red light is used instead of blue light in a convex lens, the focal length of the lens will increase.

### Answer:
The focal length will **increase** when red light is used instead of blue light in a convex lens.

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