Step 1: Understand what microwaves are.
Microwaves are electromagnetic waves with wavelengths ranging from about 1 mm to 1 m (frequencies 300 MHz to 300 GHz). They occupy the spectrum between radio waves and infrared light. Their key property is that they can travel in straight lines, penetrate the atmosphere, and can be focused into narrow beams.
Step 2: Analyse option (1): FM radio.
FM (Frequency Modulation) radio uses Very High Frequency (VHF) radio waves, typically in the range 87.5 to 108 MHz, which have wavelengths of about 3 metres. These are radio waves, not microwaves. So FM radio does not use microwaves.
Step 3: Analyse option (2): Eye surgery.
Eye surgery (such as LASIK) uses ultraviolet laser light. Microwaves are not used for eye surgery because they do not have the precision needed at the cellular level for such delicate operations. This option is incorrect.
Step 4: Analyse option (3): Cancer treatment.
Cancer treatment typically uses gamma rays or X-rays in radiotherapy because these high-energy radiations can destroy cancer cells. While some experimental microwave-based treatments exist, this is not the standard answer in this context.
Step 5: Analyse option (4): Radar system.
RADAR stands for Radio Detection And Ranging. Radar systems use microwaves because microwaves can be transmitted as narrow beams, reflected off distant objects, and their travel time gives precise distance measurements. They also penetrate clouds and rain effectively, making them ideal for detection and navigation.
Step 6: Conclude the correct use.
Among all the options, radar systems are the most well-established and standard application of microwaves. \[ \boxed{\text{Radar system}} \]