The Thorlabs kit looks like a very decent Michelson interferometer that can be used for a lot of demonstrations such as measuring wavelengths and studying the coherence properties of light sources.
However, repeating the Michelson-Morley experiment is not easy since the expected signal is very small. If there was a stationary aether, the relative length difference for the optical path along the earth's motion compared to the path perpendicular would be (v/c)^2 ≈ 1E-8, where v is the orbital velocity of earth (3E4 m/s), and c is the speed of light (3E8 m/s). The arm length of the Thorlabs kit is just a few cm, so the shift would be on the order of one nm, or one five-hundreth of a (green) wavelength. Thermal drifts and vibrations of optics on a typical optical table are much larger than that, especially when trying to rotate the setup. Michelson and Morley achieved the necessary stability by constructing their interferometer on a solid stone slab, and made a near-frictionless bearing by floating it on mercury. The resulting stability is still impressive by modern standards, but the construction technique is not very practical. Nowadays, large and passively stable optics setups (for example telescope mirrors or laser gyros) are usually made from massive pieces of Zerodur which has near-zero thermal expansion.
However, repeating the Michelson-Morley experiment is not easy since the expected signal is very small. If there was a stationary aether, the relative length difference for the optical path along the earth's motion compared to the path perpendicular would be (v/c)^2 ≈ 1E-8, where v is the orbital velocity of earth (3E4 m/s), and c is the speed of light (3E8 m/s). The arm length of the Thorlabs kit is just a few cm, so the shift would be on the order of one nm, or one five-hundreth of a (green) wavelength. Thermal drifts and vibrations of optics on a typical optical table are much larger than that, especially when trying to rotate the setup. Michelson and Morley achieved the necessary stability by constructing their interferometer on a solid stone slab, and made a near-frictionless bearing by floating it on mercury. The resulting stability is still impressive by modern standards, but the construction technique is not very practical. Nowadays, large and passively stable optics setups (for example telescope mirrors or laser gyros) are usually made from massive pieces of Zerodur which has near-zero thermal expansion.