Light — Lenses
Introduction
A lens is a transparent refracting medium bounded by two curved surfaces (usually spherical). In ICSE Class 10 Physics, you study the two types of lenses, their image-forming properties, and the mathematical relationships governing them.
Types of Lenses
Convex Lens (Converging Lens)
- Thicker at the centre than at the edges.
- Converges parallel light rays to the principal focus.
- Has a real focus.
Concave Lens (Diverging Lens)
- Thinner at the centre than at the edges.
- Diverges parallel light rays.
- Has a virtual focus.
Key Terms
| Term | Definition |
|---|---|
| Optical centre (O) | Central point of the lens |
| Principal axis | Line joining centres of curvature of the two surfaces |
| Principal focus (F) | Point where parallel rays converge (convex) or appear to diverge from (concave) |
| Focal length (f) | Distance from optical centre to principal focus |
| Radius of curvature (R) | Distance from the centre of curvature to the lens surface |
Rules for Ray Diagrams (Convex Lens)
- A ray parallel to the principal axis passes through the focus after refraction.
- A ray passing through the optical centre goes straight without deviation.
- A ray passing through the focus emerges parallel to the principal axis.
Image Formation by Convex Lens
| Object position | Image position | Nature | Size |
|---|---|---|---|
| At infinity | At F | Real, inverted | Highly diminished |
| Beyond 2F | Between F and 2F | Real, inverted | Diminished |
| At 2F | At 2F | Real, inverted | Same size |
| Between F and 2F | Beyond 2F | Real, inverted | Enlarged |
| At F | At infinity | Real, inverted | Highly enlarged |
| Between O and F | On same side | Virtual, erect | Enlarged |
Lens Formula
1 / v − 1 / u = 1 / f
Where:
- u = object distance from optical centre
- v = image distance from optical centre
- f = focal length
Sign convention (Cartesian): Distances measured against the direction of incident light are negative.
Magnification
m = v / u = hᵢ / hₒ
- m > 1 → image is larger than object.
- m < 1 → image is smaller than object.
- m positive → virtual and erect.
- m negative → real and inverted.
Power of a Lens
P = 1 / f (where f is in metres)
- Unit: Dioptre (D)
- Convex lens: P is positive.
- Concave lens: P is negative.
- 1 D = 1 m⁻¹
Worked Numericals
Example 1: Convex Lens
An object is placed 30 cm from a convex lens of focal length 20 cm. Find the image distance, nature, and magnification.
Solution: u = −30 cm, f = +20 cm 1/v − 1/(−30) = 1/20 1/v + 1/30 = 1/20 1/v = 1/20 − 1/30 = (3 − 2)/60 = 1/60 v = 60 cm (positive → real image on the opposite side)
m = v/u = 60/(−30) = −2 (negative → inverted, |m| > 1 → enlarged)
Nature: Real, inverted, enlarged
Example 2: Concave Lens
An object is placed 25 cm from a concave lens of focal length 10 cm. Find the image distance.
Solution: u = −25 cm, f = −10 cm (concave lens) 1/v − 1/(−25) = 1/(−10) 1/v + 1/25 = −1/10 1/v = −1/10 − 1/25 = (−5 − 2)/50 = −7/50 v = −7.14 cm (negative → image on the same side as object, virtual)
Common Mistakes and Fixes
| Mistake | Fix |
|---|---|
| Wrong sign for f in concave lens | f is always negative for concave lens |
| Forgetting the − sign in lens formula | 1/v − 1/u = 1/f (not 1/v + 1/u) |
| Incorrect sign for u | u is always negative (Cartesian convention) |
| Confusing real and virtual images | Positive v = real; negative v = virtual |
ICSE Exam Focus
This chapter carries 6–8 marks. Key topics: ray diagrams for convex/concave lenses, lens formula numericals, magnification, and power.
Marks Blueprint: Ray diagrams — 3 marks, Lens formula numericals — 3 marks, Power and magnification — 2 marks.
Self-Test Questions
-
An object is placed 20 cm from a convex lens of focal length 15 cm. Find the image distance and magnification.
-
A concave lens of focal length 15 cm forms an image 10 cm from the lens. Find the object distance.
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Draw ray diagrams for a convex lens when the object is at (a) 2F and (b) between F and O.
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The power of a lens is +2.5 D. What type of lens is it? Find its focal length.
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Explain the difference between a convex and concave lens with respect to their focus and image-forming ability.
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A lens forms a virtual, erect, and diminished image. Identify the type of lens.
