Option 1: Reflector versus refractor.
Step 1: Advantages of the reflecting type.
Its objective is a mirror, not a lens, and this removes the main weaknesses of a refractor. A mirror reflects every wavelength identically, so images are free of colour fringing (no chromatic aberration); a parabolic profile also kills spherical aberration. A heavy mirror can rest on a full backing plate, so very large apertures are practical, giving more collected light and finer detail. Only one face needs figuring, cutting cost and defects. A refractor's lens, by contrast, disperses colours, can only be edge-mounted (so it bends under gravity when large) and needs two accurately curved faces.
Step 2: Ray path in a refractor at normal adjustment (final image at infinity).
Take a big long-focus converging objective (\(f_o\)) and a small short-focus converging eyepiece (\(f_e\)). A distant point sends in essentially parallel rays; the objective brings them to a real, inverted, small image in its focal plane. Slide the eyepiece so its own focal plane coincides with that image. Any ray leaving that focal point then exits the eyepiece parallel to the axis, so the eye (relaxed, focused at infinity) sees a large virtual image at infinity. The tube length is \(L = f_o + f_e\) and the angular magnification is \(M = f_o/f_e\).
Schematically: parallel rays \(\Rightarrow\) objective \(\Rightarrow\) inverted real image at common focus \(\Rightarrow\) eyepiece \(\Rightarrow\) parallel emergent rays \(\Rightarrow\) image at infinity.
Option 2: Polarised light.
Step 1: What polarisation means.
An electromagnetic wave vibrates its electric field at right angles to the way it travels. Natural light contains such vibrations pointing every which way around the axis of travel. Selecting or producing light whose electric vibration keeps to a single fixed plane is called polarising the light; the beam is then plane polarised. Only transverse waves allow this.
Step 2: Sound.
Sound is a pressure wave in which particles oscillate back and forth along the propagation direction, i.e. it is longitudinal. A longitudinal disturbance has no sideways vibration to single out, so sound cannot be polarised. Hence the ability to polarise light shows light is transverse.
Step 3: Getting polarised light on refraction.
Shine ordinary light onto glass. Part reflects, part refracts, and both come out partly polarised. There is a particular incidence angle, the Brewster or polarising angle \(i_p\), where the reflected ray is fully plane polarised and stands at \(90^\circ\) to the refracted ray. Since the reflection strips the vibrations lying in the plane of incidence out of the reflected beam, those vibrations are pushed into the refracted beam; sending the light through several such plates in turn leaves the transmitted (refracted) beam highly polarised. The polarising angle obeys Brewster's law, with \(n\) the refractive index:
\[n = \tan i_p\]
\[\boxed{M = f_o/f_e; \qquad n = \tan i_p}\]