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Optical Instruments

7.2 Optical Instruments
SCIENCE • Form 5 • Chapter 7: Light and Optics

7.2 Optical Instruments

Optical instruments such as magnifying glasses, compound microscopes, and astronomical telescopes use convex lenses to form images suited to their specific functions. The size, orientation, and nature of the images depend on the position of the object relative to the focal point of each lens. Technological developments have also introduced ultra-thin lenses in everyday gadgets such as smartphones, CCTV systems, and DSLR cameras.

Learning Objectives

  • Describe the image formation and characteristics of the final image produced by a microscope.
  • Calculate the magnifying power of a compound microscope using the magnifying powers of its objective lens and eyepiece.
  • Describe the image formation, image characteristics, and normal adjustment condition of an astronomical telescope.
  • Explain the applications of lenses in optical instruments including DSLR cameras, CCTV cameras, and spy cameras.

Comparison of Ray Diagrams: Microscope vs Astronomical Telescope

How two convex lenses work together to form the first intermediate image and the virtual final image.

Comparison of ray diagrams for a microscope and an astronomical telescope A side-by-side diagram comparing a compound microscope and an astronomical telescope. Each instrument has an objective lens and an eyepiece. The microscope places the object between F sub o and 2F sub o, forming a real, inverted, magnified intermediate image beyond 2F sub o; the eyepiece then forms a virtual, magnified final image. The telescope receives parallel rays from a distant object, forms a real, inverted, diminished intermediate image at F sub o, and in normal adjustment the eyepiece forms a virtual, magnified final image at infinity with lens separation equal to f sub o plus f sub e. Microscope Astronomical Telescope Objective Eyepiece Objective Eyepiece F₀ Fₑ F₀ Fₑ Object between F₀ and 2F₀ I₀: real, inverted, magnified Final image: virtual, inverted, magnified Parallel rays from object at infinity I₀ at F₀: real, inverted, diminished Normal adjustment: f₀ + fₑ

Short Explanation

How Optical Instruments Work

Both microscopes and telescopes utilise two convex lenses: an objective lens and an eyepiece. In a microscope, the objective lens forms a real, inverted, magnified image, which is positioned within the focal length of the eyepiece to produce a highly magnified virtual final image. In an astronomical telescope, parallel rays from an object at infinity form a real, inverted, diminished image at \(F_o\). In normal adjustment, \(F_o\) coincides with \(F_e\), making the distance between lenses equal to \(f_o + f_e\), and the eyepiece forms a magnified virtual image at infinity for relaxed viewing.

Formation of the Final Image by a Microscope

A compound microscope consists of two convex lenses: an objective lens and an eyepiece.

1. Objective Lens

Object position: between \(F_o\) and \(2F_o\). First image \(I_o\) position: further than \(2F_o\). First image characteristics: real, inverted, and magnified.

2. Eyepiece

The first image \(I_o\) acts as the object for the eyepiece. Object position: between \(F_e\) and the optical centre \(O\). Final image \(I\) position: further than \(F_e\). Final image characteristics: virtual, upright relative to the first image, and magnified. Relative to the original object, the final image is virtual, inverted, and magnified.

Determining the Magnifying Power of a Microscope

\[\text{Magnifying power of microscope} = \text{Magnifying power of objective lens} \times \text{Magnifying power of eyepiece}\]

Worked example: Eyepiece magnifying power = \(4\text{ times}\), objective lens magnifying power = \(40\text{ times}\). Calculation: \(40 \times 4 = 160\text{ times}\).

Formation of the Final Image by an Astronomical Telescope

A simple astronomical telescope consists of two convex lenses: an objective lens and an eyepiece.

1. Objective Lens

Object position: at infinity, so parallel incident rays arrive from a distant object. First image \(I_o\) position: at the focal point of the objective lens \(F_o\). First image characteristics: real, inverted, and diminished.

2. Eyepiece

The first image \(I_o\) acts as the object for the eyepiece and is positioned at the focal point of the eyepiece \(F_e\). Final image \(I\) position: at infinity. Final image characteristics: virtual, upright relative to the first image, and magnified. Relative to the distant object, the final image is virtual, inverted, and magnified at infinity.

Normal Adjustment

Distance between objective lens and eyepiece = \(f_o + f_e\), where \(f_o\) is the focal length of the objective lens and \(f_e\) is the focal length of the eyepiece. The purpose of normal adjustment is to enable the image at infinity to be viewed comfortably by the human eye.

Activity 7.3: Building a Simple Telescope Model

Materials and apparatus: hollow paper cylinder, cellophane tape, convex lens with focal length \(f_o \ge 10\text{ cm}\), convex lens with focal length \(f_e \le 2\text{ cm}\), ruler, scissors or knife, and pencil. The telescope cylinder must be made of opaque materials, not transparent or translucent, to prevent stray external light from entering and disturbing image clarity. The separation distance between lenses in normal adjustment is \(f_o + f_e\).

Application of Lenses in Modern Optical Instruments

Smartphones & CCTV

Flat lenses with thicknesses of only several microns, where \(1\text{ micron} = 0.001\text{ mm}\), reduce device thickness and size.

DSLR Cameras

Lens focal length directly affects the field of vision. The shorter the focal length of the lens, for example \(24\text{ mm}\), the wider the field of vision. A longer focal length lens, for example \(70\text{ mm}\), produces a narrower field of vision with greater magnification of distant subjects.

Safety & Security Devices

Miniature lenses are used in high-resolution CCTV and spy cameras inside safety devices.

Water Lens

A spherical drop or container of water can act as a convex lens functioning as a magnifying glass under sunlight.

Try to Answer First

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

1

What is the distance between the objective lens and eyepiece of an astronomical telescope in normal adjustment?

Answer: The distance is \(f_o + f_e\), where \(f_o\) is the focal length of the objective lens and \(f_e\) is the focal length of the eyepiece.
2

Calculate the total magnifying power of a microscope that has an objective lens with a magnification of \(10\times\) and an eyepiece of \(15\times\).

Answer: Total magnifying power = \(10 \times 15 = 150\text{ times}\).
3

How does reducing the focal length of a camera lens affect its field of vision?

Answer: A shorter focal length produces a wider field of vision.

Common Mistakes

  • !Confusing the role and position of the first image \(I_o\). Students often forget that \(I_o\) acts as the object for the eyepiece lens.
  • !Calculating telescope lens separation incorrectly. Use the sum \(f_o + f_e\), not subtraction.
  • !Misunderstanding the field of view in photography. A shorter focal length actually produces a wider field of vision, not a longer one.

Concept Misunderstandings

Misconception

The final image produced by an astronomical telescope is upright compared to the original object in the sky.

Correct Concept

The final image is upright relative to the first intermediate image, but inverted relative to the original distant object.

Misconception

In a microscope, the object is placed at the focal point \(F_o\).

Correct Concept

The object must be placed between \(F_o\) and \(2F_o\) so that the objective lens produces a real, magnified intermediate image.

Summary

  • Microscope: Uses two convex lenses with \(f_o < f_e\). The intermediate image is real, inverted, and magnified. The final image is virtual, inverted relative to the object, and magnified.
  • Magnification formula: \(\text{Magnifying power} = \text{Power of objective lens} \times \text{Power of eyepiece}\).
  • Astronomical Telescope: Uses two convex lenses with \(f_o > f_e\). The intermediate image forms at \(F_o\). In normal adjustment, lens separation \(= f_o + f_e\), and the final virtual image forms at infinity.
  • Field of vision: In cameras, a shorter lens focal length gives a wider field of vision.

Short Activity

A. Objective Quiz

1 What is the separation distance between the objective lens and the eyepiece in an astronomical telescope during normal adjustment?

2 A DSLR camera user replaces a \(70\text{ mm}\) focal length lens with a \(24\text{ mm}\) focal length lens. What is the effect on the field of vision?

B. Fill in the Blanks

3 If a microscope has an objective lens with a magnifying power of 40 times and an eyepiece of 4 times, its total magnifying power is times.

 

4 In a simple telescope model, the cylinder must be made of materials so that unwanted external light does not enter.

 

C. Drag and Drop: Match the Instrument or Parameter to Its Function

Drag each item to the correct function or characteristic. On a phone, tap an answer first, then tap a matching box. Tap the Answer Choices area to return a selected item.

Parameter / Instrument
Objective lens of microscope
Normal adjustment of telescope
Short focal length camera lens
Micron-thick flat lens
Function or Characteristic
1 Forms a real, inverted, and magnified intermediate image between F and 2F
2 Lens separation distance equals fo + fe to view the image comfortably at infinity
3 Produces a wider field of vision
4 Enables smartphones and CCTV cameras to be extremely thin and compact

C. Match the Instrument or Parameter to Its Function

Write the correct item next to each function or characteristic.

Function or Characteristic Parameter / Instrument
1. Forms a real, inverted, and magnified intermediate image between F and 2F  
2. Lens separation distance equals fo + fe to view the image comfortably at infinity  
3. Produces a wider field of vision  
4. Enables smartphones and CCTV cameras to be extremely thin and compact  

Answer choices: Objective lens of microscope • Normal adjustment of telescope • Short focal length camera lens • Micron-thick flat lens

Keywords

Objective lens Eyepiece Normal adjustment Magnifying power Field of vision
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

Optical Instruments

7.2 Optical Instruments
SCIENCE • Form 5 • Chapter 7: Light and Optics

7.2 Optical Instruments

Optical instruments such as magnifying glasses, compound microscopes, and astronomical telescopes use convex lenses to form images suited to their specific functions. The size, orientation, and nature of the images depend on the position of the object relative to the focal point of each lens. Technological developments have also introduced ultra-thin lenses in everyday gadgets such as smartphones, CCTV systems, and DSLR cameras.

Learning Objectives

  • Describe the image formation and characteristics of the final image produced by a microscope.
  • Calculate the magnifying power of a compound microscope using the magnifying powers of its objective lens and eyepiece.
  • Describe the image formation, image characteristics, and normal adjustment condition of an astronomical telescope.
  • Explain the applications of lenses in optical instruments including DSLR cameras, CCTV cameras, and spy cameras.

Comparison of Ray Diagrams: Microscope vs Astronomical Telescope

How two convex lenses work together to form the first intermediate image and the virtual final image.

Comparison of ray diagrams for a microscope and an astronomical telescope A side-by-side diagram comparing a compound microscope and an astronomical telescope. Each instrument has an objective lens and an eyepiece. The microscope places the object between F sub o and 2F sub o, forming a real, inverted, magnified intermediate image beyond 2F sub o; the eyepiece then forms a virtual, magnified final image. The telescope receives parallel rays from a distant object, forms a real, inverted, diminished intermediate image at F sub o, and in normal adjustment the eyepiece forms a virtual, magnified final image at infinity with lens separation equal to f sub o plus f sub e. Microscope Astronomical Telescope Objective Eyepiece Objective Eyepiece F₀ Fₑ F₀ Fₑ Object between F₀ and 2F₀ I₀: real, inverted, magnified Final image: virtual, inverted, magnified Parallel rays from object at infinity I₀ at F₀: real, inverted, diminished Normal adjustment: f₀ + fₑ

Short Explanation

How Optical Instruments Work

Both microscopes and telescopes utilise two convex lenses: an objective lens and an eyepiece. In a microscope, the objective lens forms a real, inverted, magnified image, which is positioned within the focal length of the eyepiece to produce a highly magnified virtual final image. In an astronomical telescope, parallel rays from an object at infinity form a real, inverted, diminished image at \(F_o\). In normal adjustment, \(F_o\) coincides with \(F_e\), making the distance between lenses equal to \(f_o + f_e\), and the eyepiece forms a magnified virtual image at infinity for relaxed viewing.

Formation of the Final Image by a Microscope

A compound microscope consists of two convex lenses: an objective lens and an eyepiece.

1. Objective Lens

Object position: between \(F_o\) and \(2F_o\). First image \(I_o\) position: further than \(2F_o\). First image characteristics: real, inverted, and magnified.

2. Eyepiece

The first image \(I_o\) acts as the object for the eyepiece. Object position: between \(F_e\) and the optical centre \(O\). Final image \(I\) position: further than \(F_e\). Final image characteristics: virtual, upright relative to the first image, and magnified. Relative to the original object, the final image is virtual, inverted, and magnified.

Determining the Magnifying Power of a Microscope

\[\text{Magnifying power of microscope} = \text{Magnifying power of objective lens} \times \text{Magnifying power of eyepiece}\]

Worked example: Eyepiece magnifying power = \(4\text{ times}\), objective lens magnifying power = \(40\text{ times}\). Calculation: \(40 \times 4 = 160\text{ times}\).

Formation of the Final Image by an Astronomical Telescope

A simple astronomical telescope consists of two convex lenses: an objective lens and an eyepiece.

1. Objective Lens

Object position: at infinity, so parallel incident rays arrive from a distant object. First image \(I_o\) position: at the focal point of the objective lens \(F_o\). First image characteristics: real, inverted, and diminished.

2. Eyepiece

The first image \(I_o\) acts as the object for the eyepiece and is positioned at the focal point of the eyepiece \(F_e\). Final image \(I\) position: at infinity. Final image characteristics: virtual, upright relative to the first image, and magnified. Relative to the distant object, the final image is virtual, inverted, and magnified at infinity.

Normal Adjustment

Distance between objective lens and eyepiece = \(f_o + f_e\), where \(f_o\) is the focal length of the objective lens and \(f_e\) is the focal length of the eyepiece. The purpose of normal adjustment is to enable the image at infinity to be viewed comfortably by the human eye.

Activity 7.3: Building a Simple Telescope Model

Materials and apparatus: hollow paper cylinder, cellophane tape, convex lens with focal length \(f_o \ge 10\text{ cm}\), convex lens with focal length \(f_e \le 2\text{ cm}\), ruler, scissors or knife, and pencil. The telescope cylinder must be made of opaque materials, not transparent or translucent, to prevent stray external light from entering and disturbing image clarity. The separation distance between lenses in normal adjustment is \(f_o + f_e\).

Application of Lenses in Modern Optical Instruments

Smartphones & CCTV

Flat lenses with thicknesses of only several microns, where \(1\text{ micron} = 0.001\text{ mm}\), reduce device thickness and size.

DSLR Cameras

Lens focal length directly affects the field of vision. The shorter the focal length of the lens, for example \(24\text{ mm}\), the wider the field of vision. A longer focal length lens, for example \(70\text{ mm}\), produces a narrower field of vision with greater magnification of distant subjects.

Safety & Security Devices

Miniature lenses are used in high-resolution CCTV and spy cameras inside safety devices.

Water Lens

A spherical drop or container of water can act as a convex lens functioning as a magnifying glass under sunlight.

Try to Answer First

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

1

What is the distance between the objective lens and eyepiece of an astronomical telescope in normal adjustment?

Answer: The distance is \(f_o + f_e\), where \(f_o\) is the focal length of the objective lens and \(f_e\) is the focal length of the eyepiece.
2

Calculate the total magnifying power of a microscope that has an objective lens with a magnification of \(10\times\) and an eyepiece of \(15\times\).

Answer: Total magnifying power = \(10 \times 15 = 150\text{ times}\).
3

How does reducing the focal length of a camera lens affect its field of vision?

Answer: A shorter focal length produces a wider field of vision.

Common Mistakes

  • !Confusing the role and position of the first image \(I_o\). Students often forget that \(I_o\) acts as the object for the eyepiece lens.
  • !Calculating telescope lens separation incorrectly. Use the sum \(f_o + f_e\), not subtraction.
  • !Misunderstanding the field of view in photography. A shorter focal length actually produces a wider field of vision, not a longer one.

Concept Misunderstandings

Misconception

The final image produced by an astronomical telescope is upright compared to the original object in the sky.

Correct Concept

The final image is upright relative to the first intermediate image, but inverted relative to the original distant object.

Misconception

In a microscope, the object is placed at the focal point \(F_o\).

Correct Concept

The object must be placed between \(F_o\) and \(2F_o\) so that the objective lens produces a real, magnified intermediate image.

Summary

  • Microscope: Uses two convex lenses with \(f_o < f_e\). The intermediate image is real, inverted, and magnified. The final image is virtual, inverted relative to the object, and magnified.
  • Magnification formula: \(\text{Magnifying power} = \text{Power of objective lens} \times \text{Power of eyepiece}\).
  • Astronomical Telescope: Uses two convex lenses with \(f_o > f_e\). The intermediate image forms at \(F_o\). In normal adjustment, lens separation \(= f_o + f_e\), and the final virtual image forms at infinity.
  • Field of vision: In cameras, a shorter lens focal length gives a wider field of vision.

Short Activity

A. Objective Quiz

1 What is the separation distance between the objective lens and the eyepiece in an astronomical telescope during normal adjustment?

2 A DSLR camera user replaces a \(70\text{ mm}\) focal length lens with a \(24\text{ mm}\) focal length lens. What is the effect on the field of vision?

B. Fill in the Blanks

3 If a microscope has an objective lens with a magnifying power of 40 times and an eyepiece of 4 times, its total magnifying power is times.

 

4 In a simple telescope model, the cylinder must be made of materials so that unwanted external light does not enter.

 

C. Drag and Drop: Match the Instrument or Parameter to Its Function

Drag each item to the correct function or characteristic. On a phone, tap an answer first, then tap a matching box. Tap the Answer Choices area to return a selected item.

Parameter / Instrument
Objective lens of microscope
Normal adjustment of telescope
Short focal length camera lens
Micron-thick flat lens
Function or Characteristic
1 Forms a real, inverted, and magnified intermediate image between F and 2F
2 Lens separation distance equals fo + fe to view the image comfortably at infinity
3 Produces a wider field of vision
4 Enables smartphones and CCTV cameras to be extremely thin and compact

C. Match the Instrument or Parameter to Its Function

Write the correct item next to each function or characteristic.

Function or Characteristic Parameter / Instrument
1. Forms a real, inverted, and magnified intermediate image between F and 2F  
2. Lens separation distance equals fo + fe to view the image comfortably at infinity  
3. Produces a wider field of vision  
4. Enables smartphones and CCTV cameras to be extremely thin and compact  

Answer choices: Objective lens of microscope • Normal adjustment of telescope • Short focal length camera lens • Micron-thick flat lens

Keywords

Objective lens Eyepiece Normal adjustment Magnifying power Field of vision
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Light and Optics
Topic : Optical Equipment
Form 5 Science
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