Optical instruments — microscope, telescope, human eye comparison

medium CBSE JEE-MAIN NEET • 4 min read
Tags Optics

Question

Compare the compound microscope and astronomical telescope in terms of: (a) purpose, (b) focal length of objective vs eyepiece, (c) magnifying power formula, and (d) image characteristics. Why can’t we use a telescope as a microscope?

Solution — Step by Step

  • Compound microscope: magnifies tiny nearby objects (cells, bacteria). Object is very close to the objective.
  • Astronomical telescope: magnifies distant large objects (planets, stars). Object is essentially at infinity.
  • Human eye: has a built-in lens system with focal length that adjusts (accommodation). Normal near point = 25 cm, far point = infinity.
PropertyCompound MicroscopeAstronomical Telescope
Objective focal lengthShort (fof_o small)Long (fof_o large)
Eyepiece focal lengthShort (fef_e small)Short (fef_e small)
Magnifying powerm=Lfo×Dfem = \frac{L}{f_o} \times \frac{D}{f_e}m=fofem = \frac{f_o}{f_e}
Tube lengthL≈vo+feL \approx v_o + f_eL≈fo+feL \approx f_o + f_e
Final imageVirtual, invertedVirtual, inverted

Here LL is tube length, D=25D = 25 cm (near point), vov_o is image distance from objective.

A telescope’s objective has a large focal length — it forms a real image of distant objects near its focus. If you place a nearby tiny object in front of it, the image forms far behind the lens (if at all), and the magnification is poor. The optics are designed for a completely different scenario. Similarly, a microscope’s short-focal-length objective cannot focus parallel rays from distant objects.

Why This Works

graph TD
    A["Optical Instruments"] --> B["For nearby small objects"]
    A --> C["For distant large objects"]
    A --> D["Human Eye"]
    B --> E["Simple Magnifier: m = 1 + D/f"]
    B --> F["Compound Microscope: m = m_o × m_e"]
    C --> G["Astronomical Telescope: m = f_o/f_e"]
    C --> H["Terrestrial Telescope: uses erecting lens"]
    D --> I["Myopia: image before retina, use concave lens"]
    D --> J["Hypermetropia: image behind retina, use convex lens"]

Both the microscope and telescope use two convex lenses — but the design philosophy is opposite. A microscope needs a short-focal-length objective to produce high magnification of a nearby object. A telescope needs a long-focal-length objective to collect light from a distant object and produce a bright image.

NEET loves asking the magnifying power formula for both instruments. The most common trap: the microscope formula changes depending on whether the final image is at the near point (DD) or at infinity. At the near point: m=−vouo(1+Dfe)m = -\frac{v_o}{u_o}\left(1 + \frac{D}{f_e}\right). At infinity: m=−Lfo⋅Dfem = -\frac{L}{f_o} \cdot \frac{D}{f_e}. Always check which case the question specifies.

Alternative Method

A quick way to remember: microscope magnification depends on tube length, telescope magnification depends only on focal length ratio. If a question gives tube length, it is a microscope problem. If it gives only focal lengths of objective and eyepiece, it is likely a telescope problem.

For the telescope, to make magnification large, make fof_o large and fef_e small. For the microscope, make both fof_o and fef_e small and tube length LL large.

Common Mistake

Forgetting the sign convention in microscope magnification. The compound microscope produces an inverted image, so the magnification is negative. Many students write m=Lfo×Dfem = \frac{L}{f_o} \times \frac{D}{f_e} without the negative sign. In CBSE boards, the negative sign is expected. In JEE/NEET MCQs, the options usually give the magnitude — but read carefully whether they ask for magnification or magnifying power (magnitude).

Simple magnifier: m=1+Dfm = 1 + \frac{D}{f} (image at near point) or m=Dfm = \frac{D}{f} (image at infinity)

Compound microscope: m=−vouo(1+Dfe)m = -\frac{v_o}{u_o}\left(1 + \frac{D}{f_e}\right) or m=−Lfo⋅Dfem = -\frac{L}{f_o} \cdot \frac{D}{f_e}

Astronomical telescope: m=−fofem = -\frac{f_o}{f_e} (normal adjustment)

Tube length of telescope: L=fo+feL = f_o + f_e

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