This process occurs in the chloroplast's of the cell. These little green organelles are filled with, among other things, chlorophyll, a green fluid which is responsible for catching sun light. As you can see in the picture to the right, these are large organelles and are visible with a light microscope.

Chloroplast are responsible for photosynthesis

Chloroplast the reason for being green  

As stated in the video above

Within these chloroplast are flattened membranes called Thylakoid. These thylakoids are stacked on top of each other, forming columns through out the organelle. These columns are called granums. The light dependant stage occurs in these thylakoid membranes (click here for more detail). They are filled with chlorophyll and other light catching pigments.

The Stroma is the space within the chloroplast. This is where the Light - independent phase of photosynthesis occurs. This phase is also know as the Calvin cycle.  

Click here for information on photosynthesis

Bellow is a video about chloroplast and their role in photosynthesis