I have recently read in a book that organelles like ER (endoplasmic reticulum) and Golgi Complex cannot be seen under a compound microscope during cell division. Why does this happen, and where do the organelles go during that time?
A cell when undergoes the process of cell division there are structures known as spindle fibres that are required to pull the chromosomes off to the poles of the cell so that it can be segregated into the cells properly while division. These spindle fibres are made of microtubules that are protein molecules constituting the cytoskeleton of a cell. Endoplasmic reticulum and Golgi apparatus are also providing a lot of support to the cells. Also endoplasmic reticulum and Golgi apparatus are the sites where most of protein forms. While cell division these two organelles disintegrate so as to provide protein for microtubules formation, and so as to reduce support of the cell so the division of the cell is comparatively easier. Also, during the cell division everything divides equally between the two daughter cells, so ER and Golgi bodies disintegrate so they can be equally divided into the two daughter cells. Also, nuclear envelope is the continuation of the endoplasmic reticulum. Hence endoplasmic reticulum disintegrates with the nuclear envelope.
Here I have provided a set of possible reasons for your question.
You can refer Raven's biology for further information.