I was able to get a replacement that fit in the same mounting tabs as the original ballast. It was wider and taller than the original, but the same length.

In the Glan-Taylor polarizing prism shown on the right the rejected (ordinary) ray is absorbed by black mounting material in the prism housing.

A quarter-wave plate δ = π/2 can be used to convert linearly polarized light to circularly polarized light.  The incident linearly polarized light must be oriented at 45o to the wave plate's axes.  A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

Annoyingly true that sometimes it's cheaper to replace whole fixture than the ballast. Arrgh. LED lighting is getting cheap fast, and doesn't seem to include the environmental dangers of mercury (plus whatever evils lurk in the ballasts). Have a look here. https://www.instructables.com/howto/LED+...

In other devices the changes in direction of propagation between the two rays is used to separate the incoming beam into two orthogonally polarized beams as in the Wollaston and Thompson beam-splitting prisms.

The ballast was $18.49 at Home Depot. It did fix the issue completely, and was a lot less wasteful that throwing the entire fixture away.

The extraordinary ray violates both Snell’s Law and the Law of Reflection.  It is not necessarily confined to the plane of incidence.  Its speed changes with direction.  The index of refraction for the extraordinary ray is a continuous function of direction.  The index of refraction for the ordinary ray is independent of direction.  When the ordinary index of refraction is plotted against wavelength, the dispersion curve for the ordinary ray is a single unique curve.  The dispersion curve for the extraordinary ray is a family of curves with different curves for different directions.  A ray normally incident on a birefringent crystalline surface will be divided into two rays at the boundary, unless it is in a special polarization state or unless the crystalline surface is perpendicular to an optic axis.  The extraordinary ray will deviate from the incident direction while the ordinary ray will not.  The ordinary ray index n0 and the most extreme extraordinary ray index ne are together known as the principal indices of refraction of the material.  The direction of the lesser index is called the fast axis because light polarized in that direction has the higher speed.

A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

The good news is LED lighting is getting cheap fast. You may want to look here. https://www.instructables.com/howto/LED+...

An update: I was able to get a replacement ballast at Home Depot. The bad news is the ballast was $18.49, only $1.50 less that a whole new fixture. It took about half an hour to install the replacement ballast. The replacement was successful and the lights are working great now. In my fixture there were eight 18 gauge wires that you have to cut and then attach to the new ballast. I used wire nuts to connect the wires, so it'll be a little easier to replace the ballast again in the future.

That's what I'm afraid I'll find. Home Depot sell the whole fixture for only $20, but at least online they don't list the ballasts separately. Hopefully I can replace just the ballast, even if it costs as much as a new fixture.

The two beams within the birefringent crystal are referred to as the ordinary and extraordinary ray, respectively.  The polarization of the extraordinary ray lies in the plane containing the direction of propagation and the optic axis, and the polarization of the ordinary ray is perpendicular to this plane.

Linearly polarized light is a special case of elliptically polarized light.  If the light is linearly polarized, then the two components oscillate in phase,  for example Ex = E0xexp(i(kz - ωt)), Ey = E0yexp(i(kz - ωt)), φ = 0.  The direction of E and the direction of propagation define a plane.  The electric vector traces out a straight line.  For example, E = Ei = E0xexp(i(kz - ωt))i.

With any luck, the replacement ballast will be the same size as the old one. If it is not, you will need to find a way to secure it to the old fixture. Perhaps you will need to drill new pilot holes and use sheet metal self tapping screws. Rewire the light if you have to, plug in the new ballast, reset the breaker and you should have bright consistent light.

I had the same problem. I could not go another way because I needed the fluorescent tube to work for a UV light for my pond. That was the only way to get the light to filter my water. With LED not doing the same job. I could not go for a bulky electronic balast because of the space of a sealable unit. So I had to get this one sorted out.

When the sun is at a low angle in the sky, the sunlight reflecting off the surface of water is nearly 100% horizontally polarized because the angle of incidence is close to the Brewster angle.  Glare-reducing sunglasses are coated with a polarizer with a vertical transmission axis and therefore block the reflected light.

We've had problems for years we are fluorescent lights dimming or not coming on at times of high humidity. Sometimes I can get them on by flipping the light switch off and on several times and out of the three maybe one will only come on. This is been going on for several years and just recently the lights are getting harder and harder to turn on.

The electric field vector E can always be resolved into two perpendicular components.  The light is elliptically polarized, then the two components have a constant phase difference, and the tip of the electric field vector traces out an ellipse in the plane perpendicular to the direction of propagation.

If a beam of linearly polarized monochromatic light enters a birefringent crystal along a direction not parallel to the optical axis of the crystal, the beam will may be divided into two separate beams.  Each will be polarized at right angles to the other, and they will travel in different directions.  The intensity of the original beam will be divided between the two new beams in a manner which depends on the original orientation of the electric field vector with respect to the crystal.  The ratio or the intensities of the two orthogonally polarized beams can have any value.

The ballast is causing your problem, and it can be changed. You need to remove the original ballast, (after you shut off the circuit breaker) and take it to a lighting place or electrical supply house. Better yet, get the numbers off the ballast first and call. It may take them a little while to cross reference the part number, but they will find you a suitable replacement.

The figure below shows the trace of the field vector Ex = E0exp(i(kz - ωt)), Ey = E0exp(i(kz - ωt + φ)) in a plane perpendicular to the z-axis when looking towards the source.  (E0x = E0y = E0)

I found that this light needed a 4 micro farad capacitor with double the supply voltage of the mains connected across the Live and Neutral wire. The light flashed a few times and then can on to its full brightness. Be sure to use a ac capacitor normally comes with the light fixtures for your country and the balast wil have a drawing on it where to wire it in.

The most popular option to light large areas of buildings. They come in a variety of connection types and power ratings.

I have a fluorescent light fixture that uses two 40-watt 4' long tubes. It has recently started acting strange. When first turned on, it works fine for a minute or two, then one of the tubes becomes dim and the other becomes dim and flashing. It's not the tubes, as I've replaced those and nothing changed. Someone suggested it might be the ballast. I'm not exactly sure exactly how old the fixture is, but I'd guess it's at least 10 years old and has been used daily for that entire time. Is the problem caused by the ballast, and if so is that something that can be changed, or should I just buy a new fixture?