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

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