Lenses, Focal Length and Power
~9 min read
- Two types: Convex (converging, +ve f). Concave (diverging, -ve f).
- Lens formula: 1/v - 1/u = 1/f. Magnification m = v/u.
- Power: P = 1/f (in metres). Unit: dioptre (D). Convex has +P; concave has -P.
Lenses bend light by refraction. CDS/OTA tests image formation, lens formula, power in dioptres, and use in spectacles, cameras, microscopes and the human eye.
Convex vs Concave Lens
| Feature | Convex (Biconvex) | Concave (Biconcave) |
|---|---|---|
| Shape | Thicker in middle | Thinner in middle |
| Action | Converges parallel rays to focal point | Diverges parallel rays (appear to come from virtual focus) |
| Focal length | Positive | Negative |
| Image of distant object | Real, inverted, at focus | Virtual, erect, diminished |
| Used in | Hypermetropia (long sight), camera, microscope, magnifying glass | Myopia (short sight), peep-hole, Galilean telescope eyepiece |
Lens Formula and Magnification
- Lens formula: 1/v - 1/u = 1/f.
- Magnification: m = v/u = h_image/h_object.
- Negative m for real, inverted image; positive m for virtual, erect image.
- Lensmaker's formula: 1/f = (n-1)(1/R₁ - 1/R₂), where n is refractive index and R₁, R₂ are radii of curvature.
Power of a Lens
- Power P = 1/f (f in metres).
- SI unit: dioptre (D) = m⁻¹.
- A convex lens of focal length 50 cm = 0.5 m has P = +2 D.
- A concave lens of focal length 25 cm has P = -4 D.
- Combination of lenses: P = P₁ + P₂ + …
- Spectacle prescription gives power in dioptres.
Defects of Vision and Correction
| Defect | Cause | Correction |
|---|---|---|
| Myopia (short sight) | Image forms in front of retina. Eyeball elongated | Concave lens (diverging) |
| Hypermetropia (long sight) | Image forms behind retina. Eyeball too short | Convex lens (converging) |
| Presbyopia | Age-related loss of accommodation | Bifocal lens |
| Astigmatism | Non-spherical cornea | Cylindrical lens |
CDS/OTA PYQ Examples
Q: Power of a lens of focal length 25 cm is:
(a) +2 D (b) +4 D (c) -2 D (d) -4 D
Answer: (b) +4 D. P = 1/f = 1/0.25 = 4.
Q: Myopia is corrected by using a:
(a) Convex lens (b) Concave lens (c) Cylindrical lens (d) Bifocal lens
Answer: (b) Concave lens.
Q: SI unit of power of a lens is:
(a) Watt (b) Joule (c) Dioptre (d) Lux
Answer: (c) Dioptre = m⁻¹.
Q: A magnifying glass is a:
(a) Concave lens (b) Convex lens of short focal length (c) Plane mirror (d) Concave mirror
Answer: (b) Convex lens — object placed inside focus.
Q: In a human eye, image is formed on:
(a) Cornea (b) Iris (c) Retina (d) Pupil
Answer: (c) Retina.
Drill Lenses, Focal Length and Power for CDS/OTA
CDS/OTA-pattern items on Lenses, Focal Length and Power with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why does the focal length of a lens depend on the medium?
From the lensmaker's formula, f depends on (n_lens/n_medium - 1). A glass lens immersed in water has longer focal length because the refractive index contrast is reduced.
What is accommodation?
The eye's ability to change the focal length of its lens (by ciliary muscle contraction) so that objects at different distances form sharp images on the retina.
Why does the human eye have a least distance of distinct vision of 25 cm?
Because the maximum accommodation of the lens cannot focus objects closer than ~25 cm clearly for a normal adult eye.