Bulbs for Microscopes Has it really failed

Depends on what you want to do and how serious you are about what you have to do and whether you are likely to use a tester again.

If you need to test for the presence of low voltage a suitable bulb with two lengths of wire soldered to it will serve as a test lamp. Testing for continuity needs some sophistication adding to the basic test lamp but actually measuring voltage or resistance requires a multimeter.

I have no wish to insult you but asking your question rather indicates you wouldn't know how to use any sort of tester if you actually had one.

There are lots of books, lots of stuff online and most folk have friends, neighbours and relatives who would be only too pleased to teach you some basics and perhaps more. I suggest you engage with such sources or pay someone else to do your job.

Check the bulb, if it's intact then must be a fuse or broken wire. Use a multimeter & check continuity across all fuses if intact then trace wire back from light to switches etc

Just put a multimeter on it. 0 ohms could mean it's open circuit.
Switch multimeter to "continuity" and you should get a beep or a buzz if it's still intact. If you get nothing then it's open circuit and should be replaced. If you test it with heat you will probably burn it out if it's not already broken.

Please check using a tester/multimeter for the voltage on the bulb holder or test if the bulb within is fused or not using a continuity test. If not the fault can be with the main door switch of the fridge - normally some switches fail and so there will be no contact. If not there can be break in the circuit line/wiring to the holder.
Getting the correct type of bulb please check on this link:
http://www.espares.co.uk/search/fridges-and-freezers/p/1084

HI. The actual door switch has failed.

Test the switch for continuity using a multimeter. Set the multimeter to the ohms setting X1. Place a probe on each terminal. The multimeter should change from a reading of infinity to zero when the probes touch the terminals. With the probes still touching the terminals depress the switch, the reading should change back to infinity. If it does not pass both of these tests, the switch should be replaced