Question

\(\text{ Arrange the following in increasing order of focal length of convex lens:}\)
\((A)\) \(F_v\), focal lengths of violet
 \((B)\) \(F_r\), focal lengths of red
 \((C)\) \(F_b\), focal lengths of blue
\((D)\) \(F_y\), focal lengths of yellow
\(\text{Choose the correct answer from the options given below:}\)

• A. (A), (B), (C), (D)
• B. (C), (B), (D), (A)
• C. (B), (A), (D), (C)
• D. (A), (C), (D), (B)

Answer 1

The Correct Option is D

To determine the correct order of focal lengths for different colors in a convex lens, we need to understand how colors are refracted differently. In a convex lens, the refractive index affects the focal length for different colors in the visible spectrum.

The refractive index is higher for violet light and lower for red light, as violet light has a shorter wavelength and red has a longer wavelength.

The formula for the focal length \( f \) of a lens is related to the refractive index \( n \) by \( f \propto \frac{1}{n-1} \).
Hence, greater \( n \) implies a smaller \( f \).

The order of decreasing refractive indices and hence increasing focal lengths is:

• Violet \( (F_v) \)
• Blue \( (F_b) \)
• Yellow \( (F_y) \)
• Red \( (F_r) \)

Thus, the increasing order of focal lengths is: (A), (C), (D), (B).

Answer 2

Given: Focal lengths of a convex lens for different colors of light.

Key Concept:

For a convex lens, focal length (f) depends on the refractive index (μ) of the lens material for different wavelengths (colors). The relationship is given by the lens maker's formula:

\[ \frac{1}{f} = (μ - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]

Since μ decreases with increasing wavelength (from violet to red), focal length increases with wavelength.

Color-Wavelength Relationship:

Violet (shortest λ) < Blue < Yellow < Red (longest λ)

Therefore, focal lengths follow the reverse order:

Focal length: Violet (shortest) < Blue < Yellow < Red (longest)

Given Options:

A. F_v (violet) - shortest focal length

C. F_b (blue)

D. F_y (yellow)

B. F_r (red) - longest focal length

Increasing Order: A (violet) < C (blue) < D (yellow) < B (red)

Correct Option: (4) A, C, D, B