For a phototransistor circuit, take a look at my measurements of the AF540FGZ flash:
Pentax AF540FGZ flash. The same circuit works for even faster photodiodes. I am now using QSD2030 photodiodes, which are available from Digikey (digikey.com) - for 60 cents apiece! - and have nanosecond response. If you want one, pm me and I’ll mail you one (or I can send a SFH-309 phototransistor). I buy them by the 5 or 10, otherwise the postage is the dominant cost per unit! Data sheets for all these components are available on-line. They will help you identify which leads are which on the devices.
You bias the phototransistor with batteries or a simple dc power supply - you can buy used wall warts at Goodwill or similar for a dollar or two. Make sure you get a DC supply. Any voltage up to 12V or so should be fine.
The sensitivity of the circuit can be set by using different resistor values. The bigger the resistance, the more sensitive the circuit. Conversely, that also increases the time constant of the response. If you can stay below 10k or 20k ohms, you should be OK for shutter speed measurements. The fastest you will be trying to measure is probably 1/1000 sec, or 1000 microseconds light pulse duration.
Do a google search on “photodiode phototransistor circuits” for more info. Figure 2 in
http://denethor.wlu.ca/pc300/projects/sensors/photdiod.pdf shows my simple circuit. You don’t need to worry about any of the fancier stuff!
Just put your oscilloscope input across the resistor. In a lighted room, the phototransistor may already be conducting, giving you some voltage across the resistor. If so, turn out the lights and wave a flashlight back and forth across the transistor - you should see the scope trace go up and down. Put the scope on a slow sweep speed for this.
To measure shutter speed, open the back of the camera and place the photo detector about where the film plane would be, centered where the actual image frame would have been recorded. Take the lens off the camera and put your light source near the front of the camera, centered on the lens hole. Set your scope to single trigger on the light blip that comes through the camera when you fire the shutter and just measure the duration of the resulting pulse on the scope. Set the sweep speed consistent with the expected duration of the shutter opening.
For the fastest shutter speeds, when both shutter curtains are in motion, you have to be a bit more careful to make sure everything is lined up OK.
You should be able to measure the length of the light pulses to a few percent, which is way less than one stop.
If you can’t find your old scope or borrow one, and can generate an excuse to buy a new one (acquiring electronics test equipment can be very akin to LBA!), I’d suggest some of the new digital sampling scopes. The one I have, the Owon DS6062, was less than $400. There are several other brands with similar specs and costs. Do some checks on Ebay. The digital scopes will let you measure your light pulses at leisure. You can expand the trace on a captured signal, and there are movable measurement markers that will display the time interval for you - no interpolation necessary!
I measured an old Topcon that my father had with a system like this. The shutter speeds were reasonably close to expected up to about 1/250 sec. The last two (1/500 and 1/1000) were substantially longer than they were supposed to be.
If you have questions about the circuit or measurements, please send me a pm. Go make some measurements, and let us know how close your “new” camera is.
For DSLRs, you can’t make measurements like this. I have come up with, though, an electronic shutter speed measurement light source: an array of LEDs that steps through the LED array at a rate 50 times the expected shutter speed. You take a picture of the array and count the number of LEDs that show up. The two cameras I have measured this way (a Canon and a Pentax) were very close at all shutter speeds - within 2 or 3 % of stated value.