Which organisms can perform photosynthesis?

Eukaryotes like plants and green algae contain membrane bounded organelles which aid them to perform photosynthesis.

The process of photosynthesis is basically divided into two steps i.e Light reactions and dark reactions (known as Calvin cycle or #C_3# pathway).

During light reactions, the sunlight energy is absorbed by photosynthetic pigments. Photosynthetic pigments are present in thylakoid membranes of chloroplast. This absorbed energy is converted into chemical energy of #ATP# and #NADPH#.

And then in dark reactions this chemical energy is used to produce sugars in stroma of chloroplast. Stroma is dense fluid present within in chloroplast.

As both the reactions of photosynthesis takes place within different regions of the chloroplast so presence of chloroplast is vital for the organisms to photosynthesise their food.
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Photosynthetic prokaryotes:
Prokaryotes cyanobacteria(blue green algae) don't contain any membrane bound organelles so they also don't contain chloroplasts. But there are some prokaryotes who photosynthesize their own food. The reason for this is that they have light harvesting photosynthetic systems and unstack photosynthetic membranes which work as thylakoids for them.

Hope it helps...