I have a 4 band image (Blue, Green, Red and Near Infrared). If I display my image with only the green band in the RGB channel, the image displayed is panchromatic.
Why is that?
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An RGB image can not be rendered if you only supply information for one color channel. This is because three channels are needed: Red, Green and Blue. Different software will deal with this invalid input in different ways: Some might set the remaining channels as black (i.e. filling with zero values). In that case the resulting image will be monocromatic. In shades of green in your example.
Other software might fill the missing channels with the same information supplied for the available one. In that case the result is a gray scale version of the band supplied.
In a general case, the rendered image will only display varying colors if two or more channels contain different information (i.e. different bands).
As mentioned in the comments, it is important to note that the difference between monocromatic and pancromatic. The former is a general term used to describe images formed by shades of a single color. While the latter is a specific term used in multispectral sensors to denote a band with a wider spectral response, and that usually have also higher spatial resolution.