6.5 Optical Instruments
Optical instruments use lenses to enhance human vision by magnifying tiny specimens, bringing distant celestial objects closer, or capturing images digitally. This topic explores the structures, ray diagrams, and functions of lenses in magnifying glasses, compound microscopes, astronomical telescopes, and small camera lenses used in smartphones and CCTV systems.
Learning Objectives
- Justify the usage and functions of lenses in optical instruments such as magnifying glasses, compound microscopes, and telescopes.
- Explain the image formation, lens criteria, and normal adjustments of a compound microscope and an astronomical telescope.
- Calculate the linear magnification of an astronomical telescope at normal adjustment using the focal lengths of lenses.
- Describe the application and limitations of small lenses in modern technology, such as smartphone cameras and CCTV.
Ray Diagrams of Compound Microscope vs. Astronomical Telescope
Compare lens arrangements, focal length relationships, image positions, and characteristics between a microscope and a telescope.
Compound Microscope
Two convex lenses with short focal lengths: \(f_o < f_e\).
Distance between lenses is greater than \(f_o + f_e\).
\(f_o < u < 2f_o\).
Real, inverted, magnified; acts as object for eyepiece.
Virtual, magnified, inverted; at near point \(25\text{ cm}\).
Astronomical Telescope
Objective lens long \(f_o\), eyepiece short \(f_e\): \(f_o > f_e\).
At normal adjustment, \(L = f_o + f_e\).
Real, inverted, diminished; at focal plane \(F_o, F_e\).
Virtual, magnified, inverted; at infinity.
\(M = \dfrac{f_o}{f_e}\).
Short Explanation
Uses of Lenses in Optical Instruments
A magnifying glass is used by gemologists to identify and evaluate gemstones, and by ophthalmologists to examine eyes. A compound microscope is used by microbiologists to examine microorganisms and by geologists to study rock and mineral specimens. An astronomical telescope is used by astronomers to observe celestial objects.
Historical Milestones
In 1609, Galileo Galilei invented the telescope to observe the four moons orbiting Jupiter. In the mid-17th century, Antonie van Leeuwenhoek invented the single-lensed microscope capable of \(300\times\) linear magnification to observe and draw microorganisms.
Compound Microscope — Lens Criteria
\(f_o < f_e\)Both lenses have short focal lengths. The distance between the objective lens and eyepiece lens is greater than \(f_o + f_e\).
Astronomical Telescope — Normal Adjustment
\(L = f_o + f_e\)The objective lens has a long focal length and the eyepiece lens has a short focal length, so \(f_o > f_e\).
Magnification at Normal Adjustment
\(M = \dfrac{f_o}{f_e}\)A larger objective lens diameter collects more light, producing a brighter and clearer image.
Smartphone Cameras and CCTV
Small-sized convex lenses form a real, diminished, and inverted image on the digital sensor. The minimum distance between the sensor and the optical centre of the lens equals the focal length of the camera lens. Because the focal length cannot be zero, the overall thickness of a smartphone or CCTV is limited by the focal length of its camera lens.
Try to Answer First
Answer in your mind, then press “Check Answer”.
Why must the objective lens of an astronomical telescope have a large diameter?
Check Answer
State two differences between the lenses used in a compound microscope and an astronomical telescope regarding their focal lengths.
Check Answer
What is the formula for the magnification, \(M\), of an astronomical telescope at normal adjustment, and how is the distance between its lenses calculated?
Check Answer
Common Mistakes
- Confusing the focal length requirements: writing \(f_o > f_e\) for a microscope instead of \(f_o < f_e\).
- Assuming the distance between lenses in a compound microscope is \(f_o + f_e\). For a microscope, the distance is greater than \(f_o + f_e\) (\(D > f_o + f_e\)); it is only equal to \(f_o + f_e\) for a telescope at normal adjustment.
- Forgetting that the final image in both the compound microscope and the astronomical telescope is inverted relative to the original object, even though it is magnified.
Concept Misunderstandings
The final image formed by a compound microscope or telescope is upright because it is magnified.
The intermediate image is inverted by the objective lens, and the eyepiece acts as a magnifying glass that produces an upright image relative to the intermediate image. Therefore, the final image remains inverted compared to the original object.
Smartphones can be made infinitely thin by simply using thinner glass.
The camera sensor must be placed at a distance equal to the focal length of the convex lens to form a focused image of distant scenes. Since the focal length cannot be zero, it sets a physical lower limit on the device's thickness.
Summary
- Compound Microscope: Two convex lenses with \(f_o < f_e\) (both short focal lengths). Separation: \(D > f_o + f_e\). First image \(I_1\): real, inverted, magnified. Final image \(I_2\): virtual, magnified, inverted compared to object; formed at the near point (\(25\text{ cm}\)).
- Astronomical Telescope: Two convex lenses with \(f_o > f_e\) (\(f_o\) long, \(f_e\) short). Separation at normal adjustment: \(L = f_o + f_e\). First image \(I_1\): real, inverted, diminished (at focal plane \(F_o, F_e\)). Final image \(I_2\): virtual, magnified, inverted compared to object; formed at infinity. Magnification: \(M = \dfrac{f_o}{f_e}\).
- Smartphone Camera & CCTV: Small convex lens forms a real, diminished, inverted image on the sensor. Minimum device thickness is restricted by the focal length of the camera lens.
Short Activity
Objective: Test your understanding of optical instruments, lens arrangements, and image characteristics.
A. Objective Quiz
1 An astronomical telescope is set at normal adjustment. The focal length of the objective lens is \(80\text{ cm}\) and the focal length of the eyepiece lens is \(10\text{ cm}\). What is the distance between the two lenses?
2 What are the characteristics of the image formed on the sensor by the convex lens in a smartphone camera?
B. Fill in the Blanks
3 For a compound microscope at normal adjustment, the distance between the objective lens and the eyepiece lens must be greater than .
4 At normal adjustment, the final image formed by an astronomical telescope is located at to provide comfortable vision for the observer.
C. Matching / Drag and Drop
Match each optical instrument or feature to its correct textbook description. If using a phone, tap the answer first, then tap the matching box.
