I have to do an experiment about light. I preferred to measure the speed of light by the experiment of Michelson and Morley. When you do the experiment, it will result in an interference pattern by changing the distance of one of the mirrors. I know they had the intention to measure the speed of light relative to the ether and the earth. But how could they derive the speed of light with the resulted interference pattern?
You can't measure the speed of light with that experiment as it was originally designed. The intensity at the detector only depends on the wavelength of the light and not its speed (assuming no luminiferous aether; we now believe there is no luminiferous aether).
If there had been a luminiferous aether, then the intensity at the detector would depend both on the velocity of the luminiferous aether and the speed of light, but the velocity of the aether is unknown, so you would not be able to measure the speed of light this way anyway.
You might be able to measure the speed of light if you put the whole interferometer on an oscillating translation stage, but I am not sure how quickly you would need to oscillate it to get a good measurement of the speed of light, and you would probably need some special mirrors or lenses to keep the beams from the two arms of the interferometer overlapping on the detector even as the interferometer oscillates.
As has already been explained, MM were not specifically measuring the speed of light.
If you are still keen to measure the speed of light you could possibly get some ideas here.
A Michelson interferometer might possibly be part of your equipment.
If you have a light source of known wavelength, and you can accurately control the movement of one end of the device, you could possibly use the movement of fringes to estimate the speed of light.
I don't know what your context is. I would guess most high school labs won't have this kind of equipment in stock. Many university labs will have this or similar equipment.
Maybe there are easier ways to get an estimate, depending on what equipment you have available.
The michelson interferometer measures the relative speed of light between the 2 arms of the apparatus. The device was placed on a float on a mercury bath, such that it could be rotated.
1-If a shifting in the interference pattern had occured during the rotation it would have meant the speed of light would have changed
2-If the spread of the interference pattern would have changed in the rotation it would have meant the wavelength had changed