What is "DIN" and "JIS"? What is the difference between them?

Both DIN (Deutsches Institut für Normung) and JIS (Japanese Industrial Standards) are industry standards for microscope objectives and eyepieces.

When referring to microscopes, a DIN standard eyepiece or objective uses a basic 160mm tube length. DIN microscopes begin with an object-to-image distance of 195mm, then fix the object distance at 45mm. The remaining 150mm distance to the eyepiece field lens sets the internal real image position, which is defined as 10mm from the end of the mechanical tube (which gives the 160mm tube length). DIN standard eyepieces have an international standard 23mm diameter. DIN standard objectives often times have "DIN" etched on the side and have a standard 0.7965" diameter thread, 36 TPI, 55° Whitworth threading.

A JIS standard system has a 170mm tube length. JIS standard eyepieces also have an international standard 23mm diameter, however JIS standard fixed the object distance at 30mm. JIS standard objectives also have a standard 0.7965" diameter thread, 36 TPI, 55° Whitworth threading.

Most microscopes are DIN standard. DIN and JIS standards are interchangeable from a mechanical point-of-view. Please note, however, that the magnification of a microscope is calculated by multiplying the objective and eyepiece power together. This is assuming you have the same standard microscope, eyepiece and objective. If your eyepiece, objective, or tube length does not conform to the same standard, then recalculation of the total magnification is necessary. Also note that non-standardized microscopes exist, so be careful when choosing an eyepiece or objective.