The microscope is a machine used to study different items and chemicals, showing both their synthesis recipe and the chemicals recieved from decomposing them.
The microscope is used by putting the item you want to study in the left slot. Using the button to the right will switch between "Chemical Synthesis Machine" and "Chemical Decomposer". The first will show you the recipe to be used in the Synthesis Machine, including the required energy, the later will show you the results of decomposing said item, including (if applicable) the chance of actually getting these results.
The microscope also has a slot for your Chemist's Journal, where it will automatically store all discoveries you make.