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.
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”.
What is the distance between the objective lens and eyepiece of an astronomical telescope in normal adjustment?
Calculate the total magnifying power of a microscope that has an objective lens with a magnification of \(10\times\) and an eyepiece of \(15\times\).
How does reducing the focal length of a camera lens affect its 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
The final image produced by an astronomical telescope is upright compared to the original object in the sky.
The final image is upright relative to the first intermediate image, but inverted relative to the original distant object.
In a microscope, the object is placed at the focal point \(F_o\).
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.
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
