I have a few questions related to the emission of electromagnetic radiation by black bodies.

Consider the following image:

On the above image I have drawn the rays of light that are emmited by black bodies assuming that they have only 8 points of emmision (They are marked with red dots).
Which of these two images shows the real situation? The single point emits the radiation in all directions or only in one direction?

If my intuition is not wrong and the image on the right is correct consider the next image where I assume that there is only one point of emmission on the object:

• Is the intensity of radiation the same in every direction?
• Does the radiation in each direction have the same intensity-wavelength distribution (presented in the image below)?

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This is a difficult concept to talk about without using a few proper definitions. Unfortunately these radiometric definitions all sound very similar and have similar meanings but important differences.

Intensity is the rate of energy transfer per unit area. Intensity does not have direction and thus we cannot even talk about radiation having 'different' intensities in different directions by definition.

The radiant intensity, however, is the amount of energy transfer per unit solid angle.

The radiance is the amount of energy transfer per unit area per unit solid angle.

Lambert's cosine law states that the radiant intensity of an ideally diffuse emitter (e.g. a perfect black body) is proportional to $\cos^2\theta$, where $\theta$ is the angle from surface normal.

However, the apparent surface area of a flat object is also reduced by a factor of $\cos^2\theta$ when viewed from an angle $\theta$ from normal. Thus the radiance does not vary with angle.

When you use the term intensity in your question, you probably mean radiance, which is the most natural term to talk about. It is the same as talking about how bright an object appears. To quote wikipedia:

Radiance is useful because it indicates how much of the power emitted by an emitting or reflecting surface will be received by an optical system looking at the surface from some angle of view.

In summary:

Is the radiance the same in every direction? Yes.

Does the radiance in each direction have the same spectral distribution? Yes.

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In the classical case a single point emits in all directions.

Obviously it only emits a single photon at a time and that photon only goes in one direction, but averaged over time a blackbody emits photons in all directions with equal probability

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