In the Preferences of the Arduino IDE; after
Show verbose output during: check the box next to
Then when you compile you should get something like this at the bottom of the window:
"/Applications/Arduino.app/Contents/Java/hardware/tools/avr/bin/avr-objcopy" -O ihex -R .eeprom "/var/folders/tp/grrlc56j3z7057f12_7f1_0r0000gn/T/arduino_build_635063/Blink.ino.elf" "/var/folders/tp/grrlc56j3z7057f12_7f1_0r0000gn/T/arduino_build_635063/Blink.ino.hex"
Sketch uses 928 bytes (3%) of program storage space. Maximum is 30720 bytes.
Global variables use 9 bytes (0%) of dynamic memory, leaving 2039 bytes for local variables. Maximum is 2048 bytes.
At the end of the third line from the bottom you get the
.hex filename. In this case (on OSX) that would be