Question

Arrange the following in increasing order of focal length of a given lens. (A) \(f_V\) -- focal length for violet colour (B) \(f_B\) -- focal length for blue colour (C) \(f_Y\) -- focal length for yellow colour (D) \(f_R\) -- focal length for red colour Choose the correct answer from the options given below:

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

Hint:

For a lens, \[ f\propto \frac{1}{(\mu-1)} \] Higher refractive index implies smaller focal length. Therefore, violet light has the minimum focal length and red light has the maximum focal length.

Answer 1

The Correct Option is A

Concept: The focal length of a lens depends on its refractive index. From the lens maker's formula, \[ \frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \] Thus, \[ f\propto \frac{1}{(\mu-1)} \] The refractive index of the lens material is maximum for violet light and minimum for red light. \[ \mu_V>\mu_B>\mu_Y>\mu_R \] Hence, focal length varies inversely as refractive index.

Step 1: Arrange the colours according to refractive index. \[ \mu_V>\mu_B>\mu_Y>\mu_R \]

Step 2: Arrange the focal lengths. Since \[ f\propto \frac{1}{(\mu-1)} \] the focal length will be smallest for violet light and largest for red light. \[ f_V<f_B<f_Y<f_R \]

Step 3: Write the increasing order. \[ (A)<(B)<(C)<(D) \] \[ \boxed{ f_V<f_B<f_Y<f_R } \] Hence, the correct option is \[ \boxed{(A)} \]