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
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C), (D), (B)
The focal length of a lens depends on the refractive index through the lens maker's formula.
\( \displaystyle \frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
Because of dispersion, glass has the largest refractive index for violet and the smallest for red:
\( n_v \gt n_b \gt n_y \gt n_r \)
A larger \( n \) gives a larger \( 1/f \), that is, a shorter focal length. So
\( F_v \lt F_b \lt F_y \lt F_r \)
The increasing order is (A), (C), (D), (B).
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), but it is still in the CUET 2026 syllabus, so do not skip it.
NCERT (Pre-rationalised edition, 2022-23):
Dispersion by a Prism – “… There is actually a continuous variation of colour, but broadly, the different component colours that appear in sequence are: violet, indigo, blue, green, yellow, orange and red (given by the acronym VIBGYOR). The red light bends the least, while the violet light bends the most (Fig. 9.25).”
Dispersion by a Prism – “… Dispersion takes place because the refractive index of medium for different wavelengths (colours) is different.”