Intuitive understanding of wavelength

Light is described as having wavelength. I can somewhat understand this in connection with for example the double slit experiment, that photons interact spatially in a wave like manner.

But can the wavelength of light be described in a way which more intuitively relates to the waves of sound or oceans? Does "the length" have a specific orientation relative to the path of light? Doppler shifts seem to indicate that the wavelength is measured in the direction of light's movement, the speed stretches it out. But the double slit experiment, and the shapes of antennas, seem to indicate that the wavelength is meassured perpendicular to light's movement.

How large is a photon and what shape does it have in terms of its "length"?

The wavelength of light, and for any wave in general, is measured along the direction of propagation. It has every bit of the intuitive meaning that the wavelength of a water surface wave does.

One of the most meaningful ways to visualize light is as an oscillation of the electric and magnetic fields over space and time:

(Image source)

The electric field $\vec E$, in particular, is orthogonal to the direction of propagation, along $\vec k$. This explains why antennas often have metal rods orthogonal to the direction they point in: the electric field accelerates charges along those rods and creates a voltage between their tips, which can be measured. This is not unusual for waves either: water surface waves are also transverse waves, and wave power stations also use this transverse motion.

The double slit experiment is also consistent with this fact. For one, it is perfectly easy to observe in water waves, as is done, for example, in this Veritasium video:

The reason that the wavelength gets to play a role in a direction that you perceive to be orthogonal to the propagation direction is that the double-slit interference depends on having point sources which radiate waves in all directions, so that each wave will also have a different phase at different points along the screen; the differences in these phases then make up the interference pattern.

The 'length' is indeed measured in the direction the wave is traveling. A lightwave is a transverse wave, consisting of an electric and a magnetic field. A photon can be imagined as a localized wave. Length and shape of a photon are meaningless concepts

Like KsdLingen said a photon does not really have a length or size. You could ague that this is due to its wave-particle duality (a concept from quantum mechanics).

The wavelength of a photon, $\lambda$, indicates what distance it will travel in vacuum while its electromagnetic field completes one period. The direction of these fields are always perpendicular to the motion of the photon and the electric and magnetic fields are perpendicular as well, see figure below.

The direction of these fields are vectors, so these waves do move perpendicular to the photon, but indicate the direction of the field at the photon.

• How does the photon determine which axis to vary the electrical field, and which to vary the magnetic field? Or is that diagram avoiding a level of complexity? Commented Aug 6, 2014 at 21:05
• @BenjaminWheeler yes, every photon has a specific orientation of its electricfield (and thus also its magneticfield) this is also called the polarization, this can vary between linear to circular. Commented Aug 6, 2014 at 21:30