Question

Reflecting telescopes are supposed to be better than refracting telescopes. Why? Draw the ray diagram for image formation by a refracting telescope. Final image is formed at infinity.
OR
What is the meaning of polarisation of light? Whether sound waves are also polarized? Explain polarization of light by refraction.

Hint:

Option 1: mirror objective avoids chromatic aberration and can be made large; refractor tube length = f_o + f_e with image at objective focus = eyepiece focus. Option 2: polarisation restricts transverse vibrations to one plane, sound is longitudinal so not polarisable, and Brewster's law is mu = tan i_p.

Answer 1

Option 1: Reflecting vs refracting telescope.

Step 1: Why reflecting telescopes are better.
(a) A reflecting telescope uses a concave mirror as objective, so there is no chromatic aberration (mirrors reflect all colours the same way, while a lens bends different colours by different amounts).
(b) Spherical aberration is greatly reduced by using a parabolic mirror.
(c) A large mirror can be supported all along its back surface, whereas a large lens can be held only at its rim and sags under its own weight; hence mirrors can be made much larger, giving higher light-gathering power and resolution.
(d) A mirror has only one surface to grind and polish (a lens has two), so it is cheaper and easier to make free of defects.

Step 2: Ray diagram of a refracting telescope (normal adjustment, final image at infinity), described in words.
The objective is a converging lens of large focal length \(f_o\); the eyepiece is a converging lens of small focal length \(f_e\). Parallel rays from a distant object enter the objective and converge to form a real, inverted, diminished image \(A'B'\) at its focus \(F_o\). The eyepiece is positioned so that this image \(A'B'\) lies at its focus \(F_e\) as well, i.e. the two foci coincide (length of tube \(= f_o + f_e\)). Because \(A'B'\) sits at the focus of the eyepiece, the rays leaving the eyepiece emerge parallel, so the final magnified image is formed at infinity and can be viewed by the relaxed eye.
Layout of the ray diagram:
\[ \text{Distant object} \ \to\ \text{Objective } (f_o) \ \to\ \text{real inverted image } A'B' \text{ at } F_o \equiv F_e \ \to\ \text{Eyepiece } (f_e) \ \to\ \text{parallel rays} \ \to\ \text{final image at infinity} \]
Magnifying power in normal adjustment:
\[ M = \frac{f_o}{f_e} \]

Option 2: Polarisation of light.

Step 1: Meaning of polarisation.
Light is a transverse electromagnetic wave in which the electric field vector vibrates perpendicular to the direction of propagation. In ordinary (unpolarised) light these vibrations occur in all directions in the plane perpendicular to propagation. If the vibrations are restricted to a single plane, the light is said to be plane (linearly) polarised. Polarisation is thus the confining of the field vibrations to one direction, and it is possible only for transverse waves.

Step 2: Are sound waves polarised?
No. Sound waves are longitudinal (the medium vibrates along the direction of travel), so there is no transverse vibration that can be restricted to a plane. Because polarisation requires transverse vibrations, sound waves cannot be polarised. (The fact that light can be polarised is direct proof that light is a transverse wave.)

Step 3: Polarisation by refraction / reflection (Brewster's law).
When unpolarised light strikes a transparent surface, the reflected and refracted beams are partially polarised. At one special angle of incidence, called the polarising angle (Brewster angle) \(i_p\), the reflected light becomes completely plane polarised (its vibrations are perpendicular to the plane of incidence), while the refracted light becomes maximally (partially) polarised with vibrations in the plane of incidence. At this angle the reflected and refracted rays are mutually perpendicular. Brewster's law relates \(i_p\) to the refractive index \(\mu\):
\[ \mu = \tan i_p \]
Passing light through successive refracting plates (a pile of plates) removes more and more of the in-plane vibrations from the transmitted beam, so the refracted light also becomes strongly polarised. This is polarisation by refraction.
\[\boxed{M=\dfrac{f_o}{f_e}\ (\text{telescope}); \qquad \mu=\tan i_p\ (\text{Brewster's law})}\]