Questions: Optical Instruments: Design Principles and Applications

Question 1

A biologist wants to observe structures 50 nm in size using an optical microscope with the highest available objective magnification and the sharpest lenses. Will she be able to resolve these structures?

• A. Yes — with sufficient magnification, any structure can be resolved.
• B. No — visible light has a diffraction limit of roughly 200 nm, so structures smaller than this cannot be resolved regardless of magnification.
• C. Yes — phase-contrast optics allow resolution beyond the diffraction limit.
• D. No — but only because the lens aberrations become too severe at high magnification.

Answer: (B)

Resolution is limited by diffraction: the smallest resolvable feature is approximately λ/2, which is about 200 nm for visible light (~400–700 nm wavelength). No amount of magnification can recover detail that diffraction has already blurred — magnifying a blurry image just produces a bigger blur. Electron microscopes use far shorter-wavelength electrons to break below this barrier. Phase-contrast optics improve contrast for transparent samples but do not circumvent the diffraction limit.

Question 2

A telescope's objective lens is replaced with one of the same diameter but twice the focal length, while the eyepiece stays the same. What changes?

• A. Both magnification and angular resolution double.
• B. Angular magnification doubles, but resolving power (angular resolution) is unchanged.
• C. Resolving power doubles, but magnification is unchanged.
• D. Light-gathering ability doubles because the focal length is longer.

Answer: (B)

Magnification M = f_objective / f_eyepiece, so doubling f_objective doubles M. However, resolving power is determined by the aperture (objective diameter), not focal length — the Rayleigh criterion gives minimum resolvable angle ≈ 1.22λ/D. Since the diameter D is unchanged, resolving power is unchanged. Light-gathering ability also depends only on aperture area (πD²/4), not focal length. This distinction between magnification (set by focal lengths) and resolution (set by aperture) is the central design insight of optical instruments.

Question 3

Increasing the aperture (diameter) of a telescope's objective improves both its light-gathering ability and its angular resolving power.

• T. True
• F. False

Answer: True

Both capabilities scale with aperture diameter D. Light-gathering scales as D² (area of the aperture). Resolving power follows the Rayleigh criterion: minimum resolvable angle θ ≈ 1.22λ/D — a larger D yields a smaller minimum angle, meaning finer detail can be distinguished. This is why large professional telescopes are built as large as engineering allows: aperture governs what can be seen, not just how bright.

Question 4

In a compound microscope, using a higher-power eyepiece usually reveals finer structural detail that a lower-power eyepiece would miss.

• T. True
• F. False

Answer: False

The eyepiece is a magnifying glass applied to the intermediate image formed by the objective. It can only magnify what the objective already resolved — it cannot add new information. If the objective lens has already reached its diffraction limit, a more powerful eyepiece produces 'empty magnification': a larger but equally blurry image. Resolution is determined by the objective's numerical aperture (related to its focal length and the wavelength of light), not by the eyepiece.

Question 5

Why does increasing magnification beyond a certain point fail to reveal additional detail in a light microscope?

Model answer: Magnification and resolution are independent. The objective lens sets the resolution — the finest detail it can distinguish — based on the wavelength of light and its numerical aperture (approximately λ/2 for visible light, ~200 nm). Once that limit is reached, any further magnification just enlarges the already-blurred image without recovering new information. This is called 'empty magnification.' To resolve finer detail, you must use shorter-wavelength radiation (ultraviolet, electrons) rather than higher magnification.

This is the central design constraint of all optical instruments: magnification and resolution are not the same thing. A 100× objective can resolve features a 10× objective cannot, because higher-power objectives have larger numerical apertures and shorter effective wavelengths. But switching from a 5× to a 25× eyepiece on the same objective adds no new structural information — only enlargement of the same resolution limit.