Power of a Lens

The power of a lens (P) measures its ability to bend light rays. It determines how strongly a lens converges or diverges light. The degree of convergence or divergence depends on the focal length (f).

• Convex lens (converging lens): Focuses light rays closer to the principal focus.
• Concave lens (diverging lens): Spreads light rays away from the principal focus.

Formula for Power of a Lens: \[\mathrm{P}=\frac{1}{\mathrm{f}\left(\mathrm{m}\right)}\]

where f is the focal length in metres.

SI Unit of Power:

• Dioptre (D)
• Defined as: 1D = 1m⁻¹ (A lens with a 1m focal length has a power of 1 dioptre).

Nature of Power:

• Convex lens → Power is positive (P>0).
• Concave lens → Power is negative (P<0).

Effect of Focal Length on Power:

• Shorter focal length → Higher power (greater bending of light).
• Longer focal length → Lower power (less bending of light).
• Example: A convex lens with a short focal length converges light more strongly, while a concave lens with a short focal length diverges light more strongly.

Applications:

1. It is used in eyeglasses, microscopes, telescopes, cameras, and optical instruments.
2. Higher power lenses are used for stronger corrections in vision (myopia, hyperopia).

The deviation of the incident light rays produced by a lens on refraction through it, is a measure of its power.

or

The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P.

OR

The power (P) of a thin lens is equal to the reciprocal of its focal length (f) measured in metres.

Power of lens (in D) = \[\frac{1}{\text{focal length (in metre)}}\]

or

P = \[\frac {1}{f}\]

or

P = \[\frac {1}{f (m)}\]

Power of a Lens in a Medium:

P = (n₂ - n₁)\[\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\] = \[\frac {n_1}{f}\]