Formation of Images by Lenses

7.1 Formation of Images by Lenses
SCIENCE • Form 5 • Chapter 7: Light and Optics

7.1 Formation of Images by Lenses

A lens is a transparent optical medium, such as glass, with one or two curved surfaces that refract light rays. Lenses are broadly classified into convex lenses (converging lenses) and concave lenses (diverging lenses). Understanding how lenses refract light and form real or virtual images is essential in optical instruments such as cameras, magnifying glasses, and the human eye.

Learning Objectives

  • Identify and classify the types of convex lenses (biconvex, planoconvex, convex meniscus) and concave lenses (biconcave, planoconcave, concave meniscus).
  • Explain the action of convex lenses as converging lenses and concave lenses as diverging lenses.
  • Define and explain key optical terms: optical centre (\(O\)), principal axis, axis of lens, focal point (\(F\)), focal length (\(f\)), object distance (\(u\)), and image distance (\(v\)).
  • Determine the focal length of a convex lens using a distant object.
  • Construct ray diagrams using standard principal rays for convex and concave lenses.
  • Determine the position and characteristics of images formed by convex and concave lenses at various object distances.

Summary of Ray Refraction and Image Characteristics for Convex and Concave Lenses

A side-by-side comparison of how parallel rays refract through both lens types and how the position of the object affects image properties.

Convex and concave lens ray comparison A split diagram comparing a convex lens and a concave lens. The convex lens on the left bends parallel light rays inward so they converge at a focal point on the right. The concave lens on the right bends parallel light rays outward so they appear to diverge from a focal point on the left. Convex lens Concave lens Converging lens Diverging lens Focal point, F Focal point, F Rays converge here Rays appear to diverge from here Real focus Virtual focus

Short Explanation

Definition

A lens is a transparent optical medium, such as glass, with one or two curved surfaces that refract light rays.

Lenses bend (refract) light to form images. Convex lenses bring parallel light rays together at a focal point, making them converging lenses. Depending on how far an object is placed from a convex lens, the image can be real (can be displayed on a screen) or virtual, inverted or upright, and magnified or diminished. When an object is held closer than the focal length (\(u < F\)), a convex lens acts as a magnifying glass.

In contrast, concave lenses spread light rays outward, making them diverging lenses. Because these diverging rays never physically meet after passing through the lens, they only appear to intersect when traced backwards. Therefore, a concave lens always produces an image that is virtual, upright, diminished, and located between the object and the lens, regardless of the object distance.

Two main lens types. Convex lenses are thicker in the centre and converge light rays. Concave lenses are thinner in the centre and diverge light rays.

Types of Lenses

Lenses are classified by their shape and their effect on light rays.

Convex Lens (Converging Lens)

Thicker in the centre than at the edges. Light rays converge at a focal point after passing through a convex lens.

Types: Biconvex, Planoconvex, Convex meniscus.

Concave Lens (Diverging Lens)

Thinner in the centre than at the edges. Light rays diverge after passing through a concave lens.

Types: Biconcave, Planoconcave, Concave meniscus.

Optical Terms and Their Definitions

Key optical terms used when describing lenses and image formation.
Term Definition
Optical centre (\(O\)) Point at the centre of the lens. Light rays which pass through the optical centre do not refract.
Principal axis A straight line which passes through the optical centre of a lens and the focal point (\(F\)).
Axis of lens Straight line which passes through the optical centre and is perpendicular to the principal axis.
Focal point (\(F\)) Convex lens: a point on the principal axis where light rays parallel to the principal axis converge after passing through the lens. Concave lens: a point on the principal axis where light rays parallel to the principal axis appear to diverge from it after passing through the lens.
Focal length (\(f\)) The distance between the focal point (\(F\)) and the optical centre (\(O\)).
Object distance (\(u\)) The distance between the object and the optical centre (\(O\)).
Image distance (\(v\)) The distance between the image and the optical centre (\(O\)).

Determining the Focal Length of a Convex Lens

Activity 7.2: Using a distant object to estimate the focal length.

Concept: Light rays originating from a distant object are parallel to each other.

Apparatus & Materials: Convex lens, lens holder, white screen, metre rule.

Procedure

1. Position the convex lens towards a distant object (e.g., seen through an open laboratory window).

2. Adjust the position of the white screen behind the lens until a sharp image of the distant object is formed on the screen.

3. Measure the distance between the centre of the convex lens and the screen using a metre rule. This distance is the focal length (\(f\)).

Characteristics of the image formed on the screen: Real, inverted, and diminished (formed at \(F\)).

Concave Lens Limitation: The focal length of a concave lens cannot be determined using this method because concave lenses produce virtual images that cannot be captured on a screen.

Rules for Drawing Ray Diagrams

Two standard principal rays are used to locate the image formed by a lens.

Rule 1: Parallel Ray

Convex lens: A light ray parallel to the principal axis refracts and passes through the focal point, \(F\), on the other side.

Concave lens: A light ray parallel to the principal axis refracts and appears to diverge from the focal point, \(F\), on the same side.

Rule 2: Ray Through Optical Centre

For both convex and concave lenses, a light ray heading towards the optical centre continues in a straight line through the optical centre without refracting.

Image Formation by Lenses

The position and characteristics of the image depend on the object distance.

Image Formation by Convex Lens

Image characteristics for a convex lens at different object distances.
Object Position Position of Image Characteristics
Further than \(2F\) (\(u > 2F\)) Between \(F\) and \(2F\) Real, inverted, diminished
At \(2F\) (\(u = 2F\)) At \(2F\) Real, inverted, same size as object
Between \(F\) and \(2F\) (\(F < u < 2F\)) Further than \(2F\) (\(v > 2F\)) Real, inverted, magnified
At \(F\) (\(u = F\)) At infinity Virtual, upright, magnified
Between \(F\) and optical centre (\(u < F\)) Image distance is further than \(F\) (on the same side as the object) Virtual, upright, magnified. Application: Used as a magnifying glass.

Image Formation by Concave Lens

For any object distance (e.g., \(u > 2F\) or between \(F\) and optical centre):

Position of image: Between the optical centre and focal point (\(F\)), positioned between the object and the concave lens.

Characteristics: Always virtual, upright, and diminished.

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

What type of lens is present in the human eye, and does it act as a converging or diverging lens?

Answer: The human eye contains a convex lens, which acts as a converging lens.
2

Why cannot the focal length of a concave lens be determined using a distant object and a white screen like in Activity 7.2?

Answer: A concave lens diverges light rays and forms a virtual image, which cannot be formed or projected onto a screen.
3

What must the position of the object be for a convex lens to function as a magnifying glass, and what are the characteristics of the resulting image?

Answer: The object must be placed between the focal point (\(F\)) and the optical centre (\(O\)) (i.e., object distance \(u < f\)). The characteristics of the image are virtual, upright, and magnified.

Common Mistakes

  • !Confusing focal point (\(F\)) with focal length (\(f\)): \(F\) is a specific point on the principal axis, while \(f\) is the physical distance between \(F\) and the optical centre (\(O\)).
  • !Drawing refracted rays from a concave lens as converging instead of diverging outwards as if emerging from the focal point.
  • !Assuming that light refracts at the optical centre; rays passing through the optical centre (\(O\)) continue in a straight line without refraction.
  • !Believing that concave lenses can form real, inverted images like convex lenses; concave lenses only form virtual, upright, and diminished images for all object distances.

Concept Misunderstandings

Misconception

All lenses form images on a screen.

Correct Concept

Only real images can be formed on a screen (formed by convex lenses when \(u > f\)). Virtual images (such as all images formed by concave lenses and convex lenses with \(u \le f\)) cannot be captured on a screen.

Misconception

Light rays passing through the centre of the lens bend because the glass is thickest there.

Correct Concept

Light rays that pass directly through the optical centre (\(O\)) pass straight through without bending (no refraction).

Misconception

Moving an object closer to a concave lens will eventually make the image real and inverted.

Correct Concept

For any object distance, a concave lens consistently forms a virtual, upright, and diminished image.

Summary

  • A lens is a transparent medium with one or two curved surfaces.
  • Convex lenses (biconvex, planoconvex, convex meniscus) converge light rays to a focal point \(F\); concave lenses (biconcave, planoconcave, concave meniscus) diverge light rays so they appear to come from focal point \(F\).
  • Important optical parameters include the optical centre (\(O\)), principal axis, axis of lens, focal point (\(F\)), focal length (\(f\)), object distance (\(u\)), and image distance (\(v\)).
  • The focal length of a convex lens can be estimated using light rays from a distant object focused onto a screen.
  • Ray diagrams are drawn using two standard rays: (1) ray parallel to principal axis refracts through or appears to diverge from \(F\), and (2) ray through optical centre continues straight without refraction.
  • A convex lens forms real, inverted images when \(u > f\), an image at infinity when \(u = f\), and a virtual, upright, magnified image when \(u < f\) (magnifying glass).
  • A concave lens always forms a virtual, upright, and diminished image positioned between the optical centre and the focal point.

Short Activity

A. Objective Quiz

1 What happens to parallel light rays after passing through a concave lens?

2 An object is placed at a distance of \(2F\) in front of a convex lens. What are the characteristics of the image formed?

B. Fill in the Blanks

3 The point at the centre of a lens through which light rays pass without refracting is called the .

 

4 To use a convex lens as a magnifying glass, the object must be placed between the focal point and the .

 

C. Drag and Drop: Match the Term to Its Description

Drag each term or condition to the description it matches. On a phone, tap an answer first, then tap a matching box. Tap the Answer Choices area to return a selected item.

Term / Condition
Convex lens (\(u < F\))
Concave lens (any \(u\))
Principal axis
Focal length (\(f\))
Description / Characteristic
1 Produces a virtual, upright, and magnified image
2 Produces a virtual, upright, and diminished image
3 Straight line passing through the optical centre and the focal point
4 Distance between the focal point and the optical centre

C. Match the Term to Its Description

Write the correct term or condition next to each description.

Description / Characteristic Term / Condition
1. Produces a virtual, upright, and magnified image  
2. Produces a virtual, upright, and diminished image  
3. Straight line passing through the optical centre and the focal point  
4. Distance between the focal point and the optical centre  

Answer choices: Convex lens (\(u < F\)) • Concave lens (any \(u\)) • Principal axis • Focal length (\(f\))

Keywords

Convex lens Concave lens Optical centre (\(O\)) Principal axis Focal point (\(F\)) Focal length (\(f\)) Object distance (\(u\)) Image distance (\(v\)) Real image Virtual image

Formation of Images by Lenses

7.1 Formation of Images by Lenses
SCIENCE • Form 5 • Chapter 7: Light and Optics

7.1 Formation of Images by Lenses

A lens is a transparent optical medium, such as glass, with one or two curved surfaces that refract light rays. Lenses are broadly classified into convex lenses (converging lenses) and concave lenses (diverging lenses). Understanding how lenses refract light and form real or virtual images is essential in optical instruments such as cameras, magnifying glasses, and the human eye.

Learning Objectives

  • Identify and classify the types of convex lenses (biconvex, planoconvex, convex meniscus) and concave lenses (biconcave, planoconcave, concave meniscus).
  • Explain the action of convex lenses as converging lenses and concave lenses as diverging lenses.
  • Define and explain key optical terms: optical centre (\(O\)), principal axis, axis of lens, focal point (\(F\)), focal length (\(f\)), object distance (\(u\)), and image distance (\(v\)).
  • Determine the focal length of a convex lens using a distant object.
  • Construct ray diagrams using standard principal rays for convex and concave lenses.
  • Determine the position and characteristics of images formed by convex and concave lenses at various object distances.

Summary of Ray Refraction and Image Characteristics for Convex and Concave Lenses

A side-by-side comparison of how parallel rays refract through both lens types and how the position of the object affects image properties.

Convex and concave lens ray comparison A split diagram comparing a convex lens and a concave lens. The convex lens on the left bends parallel light rays inward so they converge at a focal point on the right. The concave lens on the right bends parallel light rays outward so they appear to diverge from a focal point on the left. Convex lens Concave lens Converging lens Diverging lens Focal point, F Focal point, F Rays converge here Rays appear to diverge from here Real focus Virtual focus

Short Explanation

Definition

A lens is a transparent optical medium, such as glass, with one or two curved surfaces that refract light rays.

Lenses bend (refract) light to form images. Convex lenses bring parallel light rays together at a focal point, making them converging lenses. Depending on how far an object is placed from a convex lens, the image can be real (can be displayed on a screen) or virtual, inverted or upright, and magnified or diminished. When an object is held closer than the focal length (\(u < F\)), a convex lens acts as a magnifying glass.

In contrast, concave lenses spread light rays outward, making them diverging lenses. Because these diverging rays never physically meet after passing through the lens, they only appear to intersect when traced backwards. Therefore, a concave lens always produces an image that is virtual, upright, diminished, and located between the object and the lens, regardless of the object distance.

Two main lens types. Convex lenses are thicker in the centre and converge light rays. Concave lenses are thinner in the centre and diverge light rays.

Types of Lenses

Lenses are classified by their shape and their effect on light rays.

Convex Lens (Converging Lens)

Thicker in the centre than at the edges. Light rays converge at a focal point after passing through a convex lens.

Types: Biconvex, Planoconvex, Convex meniscus.

Concave Lens (Diverging Lens)

Thinner in the centre than at the edges. Light rays diverge after passing through a concave lens.

Types: Biconcave, Planoconcave, Concave meniscus.

Optical Terms and Their Definitions

Key optical terms used when describing lenses and image formation.
Term Definition
Optical centre (\(O\)) Point at the centre of the lens. Light rays which pass through the optical centre do not refract.
Principal axis A straight line which passes through the optical centre of a lens and the focal point (\(F\)).
Axis of lens Straight line which passes through the optical centre and is perpendicular to the principal axis.
Focal point (\(F\)) Convex lens: a point on the principal axis where light rays parallel to the principal axis converge after passing through the lens. Concave lens: a point on the principal axis where light rays parallel to the principal axis appear to diverge from it after passing through the lens.
Focal length (\(f\)) The distance between the focal point (\(F\)) and the optical centre (\(O\)).
Object distance (\(u\)) The distance between the object and the optical centre (\(O\)).
Image distance (\(v\)) The distance between the image and the optical centre (\(O\)).

Determining the Focal Length of a Convex Lens

Activity 7.2: Using a distant object to estimate the focal length.

Concept: Light rays originating from a distant object are parallel to each other.

Apparatus & Materials: Convex lens, lens holder, white screen, metre rule.

Procedure

1. Position the convex lens towards a distant object (e.g., seen through an open laboratory window).

2. Adjust the position of the white screen behind the lens until a sharp image of the distant object is formed on the screen.

3. Measure the distance between the centre of the convex lens and the screen using a metre rule. This distance is the focal length (\(f\)).

Characteristics of the image formed on the screen: Real, inverted, and diminished (formed at \(F\)).

Concave Lens Limitation: The focal length of a concave lens cannot be determined using this method because concave lenses produce virtual images that cannot be captured on a screen.

Rules for Drawing Ray Diagrams

Two standard principal rays are used to locate the image formed by a lens.

Rule 1: Parallel Ray

Convex lens: A light ray parallel to the principal axis refracts and passes through the focal point, \(F\), on the other side.

Concave lens: A light ray parallel to the principal axis refracts and appears to diverge from the focal point, \(F\), on the same side.

Rule 2: Ray Through Optical Centre

For both convex and concave lenses, a light ray heading towards the optical centre continues in a straight line through the optical centre without refracting.

Image Formation by Lenses

The position and characteristics of the image depend on the object distance.

Image Formation by Convex Lens

Image characteristics for a convex lens at different object distances.
Object Position Position of Image Characteristics
Further than \(2F\) (\(u > 2F\)) Between \(F\) and \(2F\) Real, inverted, diminished
At \(2F\) (\(u = 2F\)) At \(2F\) Real, inverted, same size as object
Between \(F\) and \(2F\) (\(F < u < 2F\)) Further than \(2F\) (\(v > 2F\)) Real, inverted, magnified
At \(F\) (\(u = F\)) At infinity Virtual, upright, magnified
Between \(F\) and optical centre (\(u < F\)) Image distance is further than \(F\) (on the same side as the object) Virtual, upright, magnified. Application: Used as a magnifying glass.

Image Formation by Concave Lens

For any object distance (e.g., \(u > 2F\) or between \(F\) and optical centre):

Position of image: Between the optical centre and focal point (\(F\)), positioned between the object and the concave lens.

Characteristics: Always virtual, upright, and diminished.

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

What type of lens is present in the human eye, and does it act as a converging or diverging lens?

Answer: The human eye contains a convex lens, which acts as a converging lens.
2

Why cannot the focal length of a concave lens be determined using a distant object and a white screen like in Activity 7.2?

Answer: A concave lens diverges light rays and forms a virtual image, which cannot be formed or projected onto a screen.
3

What must the position of the object be for a convex lens to function as a magnifying glass, and what are the characteristics of the resulting image?

Answer: The object must be placed between the focal point (\(F\)) and the optical centre (\(O\)) (i.e., object distance \(u < f\)). The characteristics of the image are virtual, upright, and magnified.

Common Mistakes

  • !Confusing focal point (\(F\)) with focal length (\(f\)): \(F\) is a specific point on the principal axis, while \(f\) is the physical distance between \(F\) and the optical centre (\(O\)).
  • !Drawing refracted rays from a concave lens as converging instead of diverging outwards as if emerging from the focal point.
  • !Assuming that light refracts at the optical centre; rays passing through the optical centre (\(O\)) continue in a straight line without refraction.
  • !Believing that concave lenses can form real, inverted images like convex lenses; concave lenses only form virtual, upright, and diminished images for all object distances.

Concept Misunderstandings

Misconception

All lenses form images on a screen.

Correct Concept

Only real images can be formed on a screen (formed by convex lenses when \(u > f\)). Virtual images (such as all images formed by concave lenses and convex lenses with \(u \le f\)) cannot be captured on a screen.

Misconception

Light rays passing through the centre of the lens bend because the glass is thickest there.

Correct Concept

Light rays that pass directly through the optical centre (\(O\)) pass straight through without bending (no refraction).

Misconception

Moving an object closer to a concave lens will eventually make the image real and inverted.

Correct Concept

For any object distance, a concave lens consistently forms a virtual, upright, and diminished image.

Summary

  • A lens is a transparent medium with one or two curved surfaces.
  • Convex lenses (biconvex, planoconvex, convex meniscus) converge light rays to a focal point \(F\); concave lenses (biconcave, planoconcave, concave meniscus) diverge light rays so they appear to come from focal point \(F\).
  • Important optical parameters include the optical centre (\(O\)), principal axis, axis of lens, focal point (\(F\)), focal length (\(f\)), object distance (\(u\)), and image distance (\(v\)).
  • The focal length of a convex lens can be estimated using light rays from a distant object focused onto a screen.
  • Ray diagrams are drawn using two standard rays: (1) ray parallel to principal axis refracts through or appears to diverge from \(F\), and (2) ray through optical centre continues straight without refraction.
  • A convex lens forms real, inverted images when \(u > f\), an image at infinity when \(u = f\), and a virtual, upright, magnified image when \(u < f\) (magnifying glass).
  • A concave lens always forms a virtual, upright, and diminished image positioned between the optical centre and the focal point.

Short Activity

A. Objective Quiz

1 What happens to parallel light rays after passing through a concave lens?

2 An object is placed at a distance of \(2F\) in front of a convex lens. What are the characteristics of the image formed?

B. Fill in the Blanks

3 The point at the centre of a lens through which light rays pass without refracting is called the .

 

4 To use a convex lens as a magnifying glass, the object must be placed between the focal point and the .

 

C. Drag and Drop: Match the Term to Its Description

Drag each term or condition to the description it matches. On a phone, tap an answer first, then tap a matching box. Tap the Answer Choices area to return a selected item.

Term / Condition
Convex lens (\(u < F\))
Concave lens (any \(u\))
Principal axis
Focal length (\(f\))
Description / Characteristic
1 Produces a virtual, upright, and magnified image
2 Produces a virtual, upright, and diminished image
3 Straight line passing through the optical centre and the focal point
4 Distance between the focal point and the optical centre

C. Match the Term to Its Description

Write the correct term or condition next to each description.

Description / Characteristic Term / Condition
1. Produces a virtual, upright, and magnified image  
2. Produces a virtual, upright, and diminished image  
3. Straight line passing through the optical centre and the focal point  
4. Distance between the focal point and the optical centre  

Answer choices: Convex lens (\(u < F\)) • Concave lens (any \(u\)) • Principal axis • Focal length (\(f\))

Keywords

Convex lens Concave lens Optical centre (\(O\)) Principal axis Focal point (\(F\)) Focal length (\(f\)) Object distance (\(u\)) Image distance (\(v\)) Real image Virtual image