What the exam asks
- Draw or complete the ray diagram for an astronomical refracting telescope in normal adjustment, and use .
- Describe the Cassegrain reflector and compare reflectors with refractors, including chromatic and spherical aberration.
- Apply the Rayleigh criterion and collecting power .
- Compare radio, infrared, ultraviolet and X-ray telescopes with optical ones: structure, position (ground or space), resolving power and collecting power.
- Explain how a CCD works and compare it with the eye for quantum efficiency, resolution, spectral range and convenience.
Core ideas
The astronomical refracting telescope
Two converging lenses: a long-focal-length objective and a short-focal-length eyepiece.
- Light from a distant star arrives as parallel rays. The objective forms a real, inverted intermediate image in its focal plane.
- In normal adjustment the principal foci of the two lenses coincide, so the lenses are apart. The intermediate image is then at the eyepiece’s focal point, the rays leave the eyepiece parallel, and the final image is at infinity. This lets a relaxed eye view it.
- Ray-diagram rules: draw parallel rays at angle to the axis, including the undeviated ray through the centre of the objective. They meet in the focal plane. The emerging rays are parallel to the line from that image point through the centre of the eyepiece, at angle .
Angular magnification is the angle subtended at the eye by the final image divided by the angle subtended at the unaided eye by the object:
This comes from the intermediate image of height : for small angles and . The final image is , which does not matter for astronomy.
The Cassegrain reflector
A concave parabolic primary mirror reflects light towards a convex secondary mirror, which intercepts it before the primary’s focus. The secondary reflects it back through a hole in the centre of the primary to a focus just behind it, at the eyepiece or camera. Folding the light path fits a long focal length into a short tube.
Aberrations
| Chromatic aberration | Spherical aberration | |
|---|---|---|
| Cause | refractive index of glass depends on wavelength, so blue light is refracted more and focuses closer to the lens than red | a spherical surface brings rays far from the axis to a focus closer to the lens or mirror than rays near the axis |
| Effect | coloured fringes and a blurred image | a blurred image with no single focal point |
| Affects | lenses only (refractors) | spherical lenses and spherical mirrors |
| Cure | achromatic doublet (lenses of two glass types), or use mirrors | use a parabolic mirror, or a smaller aperture |
Refractors against reflectors
| Refractors | Reflectors |
|---|---|
| suffer chromatic aberration | no chromatic aberration (reflection does not depend on wavelength) |
| a large lens can only be supported at its edge, so it sags and distorts under its own weight | a mirror can be supported across its whole back; large mirrors can be segmented |
| the glass must be flawless all the way through and absorbs some wavelengths, especially UV | only the front surface needs to be precise (to a fraction of a wavelength) |
| no central obstruction | the secondary mirror and its supports block some light and add diffraction effects |
| long, heavy tubes | shorter tubes; the mirror coating needs renewing |
This is why every large modern optical telescope is a reflector.
Resolving power and collecting power
Light passing through a circular aperture of diameter is diffracted. The Rayleigh criterion: two point sources are just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other. The minimum angular resolution is
A smaller means better resolution. Two stars are resolved if their angular separation is greater than or equal to .
Collecting power is the energy collected per second, which is proportional to the area of the objective, so it is proportional to . Doubling gives four times the collecting power, so fainter objects can be detected. It also halves .
Telescopes across the spectrum
| Type | Position | Structure and notes |
|---|---|---|
| Radio | ground; the atmosphere is transparent to radio waves, day and night, in cloud | a parabolic dish that focuses onto an antenna at its focus. The surface only needs to be accurate to about , so a wire mesh will do. Because is huge, even a 76 m dish has poor resolution; arrays of dishes combine signals to improve it |
| Infrared | high, dry mountains (for some wavelengths) or space | the atmosphere’s water vapour absorbs much IR. The telescope and detector must be cooled, or their own thermal radiation swamps the signal |
| Ultraviolet | space | UV is absorbed by the ozone layer. Uses reflecting optics, because glass absorbs UV |
| X-ray | space | X-rays are absorbed by the atmosphere, and would pass through or be absorbed by a normal mirror. Grazing-incidence mirrors reflect them at very shallow angles to a focus |
Space against ground. Space telescopes avoid atmospheric absorption and turbulence, and they can observe all day. But they are expensive, hard to repair and limited in size by the launch vehicle. Ground-based telescopes can be much larger and are easy to maintain.
CCDs and the eye
A charge-coupled device is a silicon chip divided into picture elements (pixels).
- Incident photons release electrons in each pixel (a photoelectric effect in silicon).
- The number of electrons released is proportional to the intensity of the light on that pixel.
- The electrons are trapped in potential wells under each pixel, so a charge pattern builds up that matches the image.
- When the exposure ends, the charge is shifted out pixel by pixel, measured, and processed into a digital image.
| Property | CCD | Eye |
|---|---|---|
| Quantum efficiency (fraction of incident photons that produce a signal) | about 80% (above 70%) | about 1% |
| Spectral range | about 400 nm to beyond 1000 nm (into the near-IR; wider with coatings) | 400–700 nm |
| Resolution | set by pixel size (about 10 μm): two images need an unilluminated pixel between them | about rad, set by the pupil and the spacing of cone cells |
| Convenience | long exposures accumulate charge, so very faint objects are recorded; the image is stored, shared and processed digitally; can be used remotely | real-time viewing with no equipment, but nothing is stored, the eye cannot build up a signal over time, and observations are subjective |
A disadvantage of CCDs is that they must be cooled to reduce thermal noise, and they need electronics and power.
Worked examples
Exam technique
- Ray diagrams: use a ruler, put arrows on the rays, make them meet exactly in the common focal plane, and draw the emerging rays parallel. Label , and both focal lengths.
- Radians only. gives radians. If a question quotes arc-seconds or degrees, convert first.
- Comparison questions reward matched pairs: “a refractor suffers chromatic aberration but a reflector does not because reflection does not depend on wavelength.”
- “Why in space?”: name the atmospheric absorber (ozone for UV; water vapour and CO₂ for IR; the whole atmosphere for X-rays), then add turbulence and day-and-night observing.
- Six-mark answers: organise them as aberrations, then mechanical and size issues, then light-gathering and cost.
Common mistakes
Quick recap
- In normal adjustment the lenses are apart, the final image is at infinity, and .