The power of a lens is defined as the reciprocal of its focal length in metres: P = 1/f. The SI unit of power of a lens is Dioptre (D), where 1 D = 1 m⁻¹. A convex (converging) lens has positive power, while a concave (diverging) lens has negative power. When lenses are placed in contact, their powers add: P = P₁ + P₂ + P₃ + ...
Power of a lens P = 1/f, where f is the focal length in metres.
SI unit of power of a lens is Dioptre (D); 1 D = 1 m⁻¹.
Convex (converging) lens has positive power; concave (diverging) lens has negative power.
Shorter focal length means greater power — a stronger lens.
For lenses in contact: P_total = P₁ + P₂ + P₃ + ...
Spectacle prescriptions use Dioptre: positive for hypermetropia, negative for myopia.
Dimensional formula of power of lens = [M⁰L⁻¹T⁰] = [L⁻¹].
Power of a Lens (P): The power of a lens is the measure of its ability to converge or diverge rays of light. It is defined as the reciprocal of the focal length.
Formula: P = 1 / f
Where: • P = power of the lens (measured in Dioptre, D) • f = focal length of the lens (must be in METRES)
Sign convention: • Convex (converging) lens: f is positive → P is positive • Concave (diverging) lens: f is negative → P is negative
Important: focal length must be in metres when calculating power in Dioptre.
If focal length is given in cm: Convert first: f(m) = f(cm) / 100 Then: P = 1 / f(m)
Example: f = 25 cm = 0.25 m P = 1 / 0.25 = +4 D (convex lens)
f = -50 cm = -0.50 m P = 1 / (-0.50) = -2 D (concave lens)
SI Unit: Dioptre (D) Also written as: diopter (American spelling) Symbol: D
Definition: 1 Dioptre = power of a lens with focal length of 1 metre 1 D = 1 m⁻¹
Note: Dioptre is NOT a base SI unit — it equals m⁻¹.
Dimensional formula of power of lens: [P] = [1/f] = [L⁻¹] = [M⁰L⁻¹T⁰]
Common power values: • +1 D → f = 1 m (weak convex lens) • +2 D → f = 0.5 m • +4 D → f = 0.25 m = 25 cm • +10 D → f = 0.1 m = 10 cm (strong convex) • −1 D → f = −1 m (weak concave lens) • −2 D → f = −0.5 m
Optician's use: Prescription lenses for spectacles are specified in Dioptres: • Positive number → convex lens → prescribed for hypermetropia (far-sightedness) • Negative number → concave lens → prescribed for myopia (near-sightedness) • Example: −2.5 D means a concave lens with f = −40 cm
When two or more thin lenses are placed in contact (touching), the equivalent power is the algebraic sum of individual powers:
P_total = P₁ + P₂ (for 2 lenses in contact) P_total = P₁ + P₂ + P₃ (for 3 lenses in contact)
Equivalent focal length: 1/f = 1/f₁ + 1/f₂ (in contact)
Example 1: A convex lens of power +3 D and concave lens of power -1 D are placed in contact. P = P₁ + P₂ = +3 + (−1) = +2 D Equivalent focal length: f = 1/P = 1/2 = 0.5 m = 50 cm (converging)
Example 2: Three lenses of powers +2 D, +3 D, −1 D placed in contact: P = 2 + 3 + (−1) = +4 D f = 1/4 = 0.25 m = 25 cm
Separated lenses (distance d apart): 1/f = 1/f₁ + 1/f₂ − d/(f₁f₂) or: P = P₁ + P₂ − d·P₁·P₂
This formula is used in compound microscopes, telescopes, and camera lens systems.
Convex (Converging) Lens: • Shape: thicker at centre, thinner at edges • Focal length (f): positive • Power: positive (e.g., +2 D, +5 D) • Converges parallel rays to a real focal point • Applications: magnifying glass, reading glasses (hypermetropia), camera lenses, projectors
Concave (Diverging) Lens: • Shape: thinner at centre, thicker at edges • Focal length (f): negative • Power: negative (e.g., −2 D, −5 D) • Diverges parallel rays as if they come from a virtual focal point • Applications: spectacles for myopia (short-sightedness), viewfinder in cameras, peepholes
Relation between focal length and power:
| Focal length | Power |
|---|---|
| Short f | High P (strong lens) |
| Long f | Low P (weak lens) |
A thicker convex lens bends light more → shorter focal length → greater positive power.
Example 1: Myopia (near-sightedness) A person cannot see objects beyond 50 cm. Far point = 50 cm = 0.50 m Required: concave lens to form image of ∞ at 50 cm f = −0.50 m P = 1/f = 1/(−0.50) = −2 D (Prescription: −2.00 D concave lens)
Example 2: Hypermetropia (far-sightedness) A person's near point is 1 m (normal near point = 25 cm). Required: convex lens to form image of 25 cm object at 1 m Using lens formula: 1/f = 1/v − 1/u 1/f = 1/(−1) − 1/(−0.25) = −1 + 4 = +3 P = +3 D (convex lens)
Example 3: Power of eye lens Human eye lens focal length varies from about 2 cm to 2.5 cm: Maximum power: P = 1/0.02 = 50 D Minimum power: P = 1/0.025 = 40 D Total power of eye (cornea + lens): ~60 D
Example 4: Combined lenses in camera Camera lens: +10 D and +5 D in contact: P = 15 D, f = 1/15 ≈ 6.67 cm
P = 1/f, where f is the focal length in metres. Power is measured in Dioptre (D).
Dioptre (D). 1 Dioptre = 1 m⁻¹. It is the power of a lens with 1 metre focal length.
P = 1/f = 1/0.25 = +4 D (converting 25 cm to 0.25 m first).
P = P₁ + P₂. For example, +3 D and −1 D lenses in contact give P = +2 D.
A concave lens has a negative focal length (by sign convention). Since P = 1/f, a negative f gives a negative power.
According to Schrödinger, a particle is equivalent to what?
Understand Schrödinger's wave mechanics. Discover why, according to Erwin Schrödinger, a particle is equivalent to a 'wave packet'.
Sign Convention for Spherical Mirrors and Lenses
Learn the New Cartesian Sign Convention for spherical mirrors and lenses. Understand when focal length (f) and image distance (v) are positive or negative.
Simple Harmonic Motion — Equation and Key Formulas
Learn the SHM equation x = A sin(ωt + φ). Understand velocity, acceleration, time period formulas and energy in simple harmonic motion for Class 11 Physics.
What is a Simple Microscope?
Learn what a simple microscope is in Physics. Understand how a single convex lens acts as a magnifying glass to see small objects, and explore its common uses.
What is the SI Unit of Density?
Learn the SI unit of density. Understand the formula (Mass/Volume), its standard unit (kg/m³), and the CGS unit (g/cm³).
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.