Astronomical Instruments
This domain tests how telescopes and detectors work and what limits them: aperture, resolution, magnification, aberrations, spectroscopy, and the atmosphere. Questions often ask you to choose the right specification for a task or to compute resolving power and magnification from given numbers.
Optics and telescope types
- Refractors use lenses and suffer chromatic aberration, which is reduced by achromatic doublets; practical apertures are limited by sagging and absorption in glass.
- Reflectors use mirrors: the Newtonian sends light out the side, the Cassegrain through a hole in the primary. No chromatic aberration; large apertures are practical.
- Aperture, not magnification, determines light grasp (proportional to D²) and resolution. Useful magnification is roughly 50× per inch of aperture at most.
- Magnification = objective focal length ÷ eyepiece focal length. Focal ratio f = F/D controls the field of view and photographic speed.
Resolution, seeing, and detectors
- The diffraction limit is θ = 1.22 λ/D in radians; Dawes' limit gives about 4.6/D arcseconds for D in inches.
- Ground-based resolution is usually capped near 1 arcsecond by atmospheric seeing; adaptive optics and space telescopes beat this.
- CCDs have quantum efficiencies above 80% versus a few percent for the eye and photographic plates; they are linear, which enables photometry.
- Spectrographs use prisms or diffraction gratings; gratings spread light into orders and give higher dispersion.
Non-optical astronomy
- The atmosphere transmits visible light, near-infrared, and radio; X-rays, ultraviolet, and most infrared require space observatories.
- Radio wavelengths are thousands of times longer than visible light, so single dishes have poor resolution; interferometry (VLA, VLBI) synthesizes a huge aperture.
- JWST observes from a 6.5 m segmented mirror at L2, optimized for infrared to see high-redshift galaxies and cool objects.
Worked example
A 200 mm (8-inch) f/10 telescope with a 20 mm eyepiece: focal length = 10 × 200 = 2000 mm, so magnification = 2000/20 = 100×. Its diffraction limit at 550 nm is θ = 1.22(5.5 × 10⁻⁷)/0.2 = 3.4 × 10⁻⁶ rad, and since 1 radian = 206,265 arcseconds, that is about 0.69 arcsecond. Under typical 1–2 arcsecond seeing the telescope is already atmosphere-limited, so buying a higher-power eyepiece would only enlarge a blurry image.
Traps that cost marks
- Maximum magnification is a marketing number; resolution and light grasp come from aperture.
- A larger aperture does not automatically mean a narrower field of view; that depends on focal length and eyepiece.
- Radio telescopes need enormous apertures because resolution scales with λ/D.
- Poor seeing cannot be fixed by magnification, only by adaptive optics, interferometry, or going to space.