Question

What happens if we paint a bulb into black color, does the bulb give the light or not? Explain.

Answer 1

A perfect black body is an ideal object which absorbs all the electromagnetic radiation regardless of the frequency and angle of incident radiation. A perfect black body neither transmit nor reflects any incident electromagnetic radiation. A perfect black body is a theoretical object and does not exist in reality. Visible light is electromagnetic radiation.

Complete step by step answer:
There are two scenarios
The bulb is painted with perfect black color,
The bulb is painted with a commercially available black color.
Case I: (Ideal case)
If a bulb is painted with a perfect black color, it will work as a perfect black body. The bulb will absorb all the visible light spectrum and will not transmit any visible light.
For perfect black body, the absorption coefficient, $\alpha = 1$
The transmission coefficient, $\tau = 0$
The reflection coefficient, $\rho = 0$
Therefore, the bulb will not give any light.
Case II:
If a bulb is painted with a commercially available black color, the bulb will work as black body. Since the bulb does not work as a perfect black body, it will absorb most of the visible light spectrum and will transmit very little or negligible visible light. The absorption $\left( \alpha \right)$, transmission $\left( \tau \right)$ and reflection $\left( \rho \right)$ coefficient of the bulb painted with black color will depend on incident light.
If the bulb has a low intensity light source (say $2watt$ rated bulb), almost all the visible light will be absorbed by the bulb and will transmit negligible or no light. Therefore, the bulb will not give any light.
If the bulb has a very high intensity light source (say $500watt$ rated bulb), the bulb will transmit some or most of the incident light. Therefore, we can see the light coming from the bulb.

Note: In both the above cases, since the bulb absorbs electromagnetic radiation, the bulb will be heated up and will emit heat radiation. The electromagnetic radiation emitted by a perfect black body is called black body radiation.
Since the black body absorbs almost all visible light, it appears to be black. Vantablack is material which absorbs $99.965\%$ of visible light.