One of the 10 -m diameter Keck telescopes can observe 500...

One of the 10 -m diameter Keck telescopes can observe 500 -nm visible-wavelength photons. If a radio telescope observing $10-\mathrm{cm}$ photons was built to be proportionally as large relative to the photons it was observing, what would its diameter be? What about a gamma-ray telescope observing 0.01 -nm photons?

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Key Concepts

Diffraction Limit

The diffraction limit is a fundamental principle in optics and telescope design that sets the smallest angular separation a telescope can resolve. It is dictated by the wavelength of the observed light and the diameter of the telescope's aperture. A longer wavelength requires a proportionally larger aperture to achieve the same resolution as a shorter wavelength.

Aperture Scaling

Aperture scaling refers to maintaining a constant ratio between the telescope’s diameter and the wavelength of light it observes. This concept means that if you design a telescope to observe a certain wavelength with an aperture of a given size, then to observe a different wavelength while achieving a similar performance, the new aperture should be scaled proportionally to the change in wavelength.

Electromagnetic Spectrum Variability

The electromagnetic spectrum spans a wide range of wavelengths—from long radio waves to very short gamma rays. Because the optimal telescope design varies with wavelength, instruments operating at different parts of the spectrum must account for these differences by adjusting parameters such as the aperture size. This explains why radio telescopes are enormous compared to optical ones, while gamma-ray detectors can be relatively tiny.

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