One common problem with many Contax and Yashica bodies is mirror slippage. The only way to properly fix the problem is to remove and refit the mirror. Warming the mirror and pushing it back into position, as many people suggest, is only a temporary solution - the mirror will slip again quite quickly. Leaving the camera on its back in a warm area, another suggested solution I've seen mentioned, might work if you can wait a few years as that's probably how long the mirror took to slip in the first place. Storing bodies on their backs is a good idea to prevent the mirror from slipping but it's not a practical solution if the slippage has already occurred.
I've seen a few other suggested ways of fixing the problem that I won't repeat here as I wouldn't want to even suggest anyone try them.
The general procedure to refit the mirror is to check the focus, remove the mirror, remove all signs of the previous adhesive tape, then refit the mirror with new, double sided, adhesive tape or cut sheet and, finally, recheck the focus. The thickness of the tape or sheet material is critical as, if it is different to the original, it will affect the focus, though this can be adjusted if necessary.
Not removing, or trying to reuse, the original adhesive will result in the mirror being refitted at an unknown distance from the carrier and, very probably, not parallel so the focus will be different at different points of the mirror. This is impossible to adjust out.
The following is how I refit mirrors. My procedure has changed a little over the years I've been doing this but this is how I do it now and it can be done without dismantling the camera. Note that the pictures shown here were taken at different times so are not necessarily a perfect sequence.
Check the focus
The point of doing this at the beginning is to create a reference that the focus can be checked against once the mirror is replaced.
With a lens attached to the camera, focus as accurately as possible on a subject a distance away but not so far away the lens is focussed very close to infinity. I use a lamppost that is about 100m away. Being a vertical target it's easy to use the split prism to focus accurately on the post. I generally use a 85mm lens. With a shorter lens a closer target would work better.
Once the lens has been focussed, look at the focus scale and record (take a photo) of the precise positioning of it.
Once the mirror has been replaced, this test can be repeated and any shift in focus easily identified.
Protect the focus screen
This is important and takes very little time to do. Although the focus screen is unlikely to become damaged, it's possible so better to protect it from the start. I do that by simply covering it with a piece of card cut to fit and extend outside the lens mount so that it can be taped in place.
Warm the mirror
It's difficult to convey how much warming is required but I use a hair drier on low for about a minute from a distance of about 15cm. Warming the mirror softens the adhesive and makes it a lot easier to remove. If you find it difficult to separate the mirror from its carrier, then try warming a little more.
Remove the mirror
Use a long, flat blade and insert it between the mirror and the carrier. Work it back and forth moving in a bit further each time until the mirror lifts up. Remove the mirror from the carrier and place it, face down, on an optical cloth or other soft cloth. Remember the mirror is coated on its upper surface so placing it face down means it will be resting on its coated surface so make sure it is resting on a suitable material and refrain from moving it around too much.
Remove the old adhesive
Some of the original tape will be left on the back of the mirror and some on the mirror carrier. Start by scraping off the remains of the tape from the back of the mirror. This can be made easier by warming it again.
Once the remains of the tape is scraped away, remove the remainder of the adhesive using a solvent such as isopropyl alcohol (IPA).
Repeat the procedure to remove the adhesive from the mirror carrier.
Again, warming the adhesive again will make it easier to remove. Once the remaining tape is removed, I use small wads of paper towel soaked in IPA held with a pair of tweezers to remove the remaining adhesive.
Cut and fit the replacement tape
First, of course, you have to obtain suitable replacement tape. The tape I use is 0.1mm thick (that's just the adhesive layer, not including the protective paper that is attached both sides). I find this works most of the time and no adjustment of the focus is necessary afterwards. But, occasionally adjustment is necessary. Whether this is because the tape used by the factory varies or whether, sometimes, it wasn't fitted flat, I don't know.
The tape I use is this one (actually its a sheet material not a tape): https://www.stix2.co.uk/product/double-sided-a4-adhesive-tape-sheets-210mm-x-297mm-a4/
There are other similar materials around which are thicker so check the thickness if you can't obtain this exact one.
Sometimes the sheet adhesive has wrinkles in it. This would stop the mirror from sitting flat so, if you get these, discard the part of the sheet with wrinkles and use a different bit.
Cut a piece of tape smaller than the mirror so that there is room at the edges to grip the mirror when refitting it.
Peel off one side of the protective sheet from the adhesive and press it onto the back of the mirror. Then remove the second protective sheet and place the mirror onto the carrier and press down gently using an optical cloth to make sure it's attached.
To handle the mirror I use a pair of, flat ended, tweezers with rubber covering on the ends. This makes it fairly easy to place the mirror into position without risk of scratching it.
Check the focus
With the mirror in position, repeat the focus check carried out at the beginning to see if there is any change. If there is, the mirror position will need adjustment. How this is done depends on the camera. Some information on adjusting the focus on the 139 is on my DIY page. Adjust the focus a little at a time, repeating the focus test each time, until you obtain the same results as were obtained at the beginning.
A note on mirror replacement
Not all mirrors are equal even if they appear to be. If you have a broken mirror and you are following this procedure to replace it. Make sure the replacement mirror is identical to the one being removed. I have found some variation in thickness of mirrors across the Contax range and a mirror of different thickness will affect the focus.