Chapter 7: Lenses

Physics | Optics | Image Formation | Complete guide to convex and concave lenses with formulas and applications

1 Introduction

A lens is a transparent optical device made of glass or plastic, bounded by two surfaces, at least one of which is curved. Lenses are used to converge or diverge light rays and form images.

Convex Lens

Also known as converging lens. Thicker at the center than edges. Converges parallel rays of light to a focus point.

Concave Lens

Also known as diverging lens. Thicker at edges than center. Diverges parallel rays of light from a focus point.

2 Convex Lens

Features:

  • Thicker at the center than edges
  • Converges parallel rays of light to a point called the principal focus (F)
  • Focal length (f) is the distance between optical center and focus

Ray Diagram Rules for Convex Lens

1

A ray parallel to the principal axis passes through the principal focus after refraction.

2

A ray passing through the optical center continues straight without deviation.

3

A ray passing through the principal focus emerges parallel to the principal axis after refraction.

Image Formation by Convex Lens

Depends on position of object:

Object Position Image Nature Image Size Image Orientation
Beyond 2F Real Diminished Inverted
At 2F Real Same size Inverted
Between F and 2F Real Magnified Inverted
At F No image formed - -
Between F and optical center Virtual Magnified Erect

3 Concave Lens

Features:

  • Thicker at edges than center
  • Diverges parallel rays of light
  • Principal focus is virtual and on the same side as the object

Ray Diagram Rules for Concave Lens

1

A ray parallel to principal axis appears to diverge from principal focus after refraction.

2

A ray passing through optical center goes straight without deviation.

3

A ray directed towards the principal focus emerges parallel to principal axis after refraction.

Image Formation by Concave Lens

Concave lenses always form:

  • Virtual image
  • Erect image
  • Diminished image
  • Image is formed on the same side as the object

4 Lens Formula

The relationship between object distance (u), image distance (v), and focal length (f) is given by the lens formula:

1/f = 1/v - 1/u
(For real is positive convention)

Sign Convention

Distances measured in the direction of incident light: Positive (+)

Distances opposite to the incident light: Negative (-)

Real images: Positive distance (v positive)

Virtual images: Negative distance (v negative)

5 Magnification

Magnification (m) is the ratio of the height of the image to the height of the object:

m = h'/h = v/u

Interpretation:

  • Positive magnification: Erect image
  • Negative magnification: Inverted image
  • |m| > 1: Magnified image
  • |m| < 1: Diminished image
  • |m| = 1: Same size image

6 Combination of Lenses

Two lenses in contact act as a single lens with combined focal length:

1/F = 1/f₁ + 1/f₂

Common Combinations:

  • Convex + Convex: Stronger converging lens (shorter focal length)
  • Convex + Concave: Reduces overall convergence (or can diverge if concave is stronger)
  • Concave + Concave: Stronger diverging lens

7 Applications of Lenses

Magnifying Glass
(Convex Lens)

Camera Lens
(Convex Lens)

Microscope
(Combination of Convex Lenses)

Eye Glasses
(Convex for hypermetropia)

Myopia Correction
(Concave Lens)

Peepholes
(Concave Lens)

Important Points for Examination

  • Draw neat, labelled ray diagrams for convex and concave lenses
  • Write lens formula and magnification formula clearly with sign conventions
  • Identify image properties based on object position
  • Use correct sign conventions in numerical calculations
  • Practice numerical problems on lens formula and magnification
  • Understand the difference between real and virtual images