Question

The numerical values of the focal lengths of two lenses A and B are 10 cm and 20 cm respectively. Which one of the two will show higher degree of convergence/divergence? Give reason to justify your answer.

Answer 1

Given:

f_A = 10 cm = 0.1 m

f_B = 20 cm = 0.2 m

Formula:

The degree of convergence or divergence of a lens is determined by its optical power P, which is given by the formula:

`P = 1/f`

where f is the focal length (in meters). A lens with a shorter focal length has a higher power and thus bends light rays more strongly.

Lens A:
`P_A = 1/f_A`

= `1/0.1`

= 10 diopters

Lens B:

`P_B = 1/f_B`

= `1/0.2`

= 5 diopters

Since Lens A has a higher power (10 diopters) than Lens B (5 diopters), Lens A shows a higher degree of convergence or divergence.

Reason:
The focal length is inversely proportional to the lens's power. A shorter focal length means that the lens can bend light more sharply, resulting in a stronger converging or diverging effect.