I drew a blank. How shutter speed needs to be at 60 to sync with the flash, but how do you determine the aperture?
I puzzled on that for a long time before I remembered that my flash had a chart that gave recommendations based on distance, ISO.
So, until I can afford to add an external flash, is there a way to compute settings with a pop up flash?
Are we still restricted to 1/60 shutter speed?
Not disagreeing with what's been said, but adding a bit specific to your questions.
We choose aperture according to the available flash power. A bit of experience quickly makes it be obvious. The internal flash is tiny, and needs wider aperture - perhaps f/4 to have enough power to be useful. An external hot shoe flash has much greater power, and can use a stopped down aperture. Except, it can do bounce flash too, which then needs much more power (up to ceiling and back), and about f/4 becomes more feasible then. But it has power to do it.
The camera metering system is ONLY about the ambient light. The camera settings it chooses is about the ambient light. This all occurs before the flash has even fired to see it. And then later, flash has its own metering system. But it has to work into the camera settings that ambient set. We might instead choose aperture more specifically to help the flash.
So for example, in a dim room where flash is needed, but without the flash yet being enabled, then perhaps it meters maybe f/5.6 at 1/4 second (just some slow shutter like that).
That is for the ambient, for a picture without the flash.
But we are not going to use the ambient, we are going to choose flash.
Reach up and enable the flash, and the shutter speed jumps to 1/60 second (in camera A or P modes). This is not about the flash exposure, and it is not about the ambient exposure. It is not metered, and not about anything, except that if you are using flash, 1/4 second is of no value to you, it might as well be 1/60. The flash is near instantaneous, and it doesn't care how long the shutter may stay open (flash exposure is not affected by shutter speed. Ambient exposure is.)
But the flash still has to work into whatever aperture was set.
We really need to choose it to help the flash.
Re: your old chart, and calculating for the flash. Your D5500 has a Guide Number of 39 (feet) at ISO 100 in Manual flash mode (spec chart in rear of manual). That is used computing this way... for a subject distance of say 6 feet, the proper aperture is GN39/6 feet = f/6.5 (camera has a f/6.3 setting). So set manual flash mode, full power level, then measure 6 feet, set f/6.3, and that distance will be exposed properly. This assumes ISO 100. If Auto ISO is on, it can be different. Manual flash mode cannot react to Auto ISO, however Nikon does not allow Auto ISO to increase at all if it sees there is a Manual flash (ISO stays at the Minimum set). Larger flashes have much higher guide numbers, much greater range. (More about Guide Numbers at
Understanding Guide Numbers including GN Calculator ).
You are not restricted to 1/60 second, that is just what the automation chooses. Camera models D7100 and up have a menu to select other (slower) values, but 1/60 is default on all. It is called a Minimum Shutter Speed With Flash. It is an arbitrary decision.
The only way to make it faster (in camera A or P modes) is to go out into brighter light that will meter higher.
But you can use camera Manual mode and set any shutter speed (any not exceeding D5500 maximum shutter sync speed of 1/200 second). The TTL flash is still automatic flash exposure in any camera mode, including Manual.
The flash exposure is not affected by shutter speed (it is faster than any shutter), but shutter speed does affect the ambient light, which indoors, is usually negligibly low, insufficient, ignorable, because we are using flash instead. If the ambient is so low, it is out of play, it does not matter what it is. We are using flash instead. (but if using fill flash out in bright sun, we obviously have to pay attention to the ambient).
Camera Manual mode is commonly used for flash indoors, so we can also affect the ambient light... which is typically orange indoors. We can keep it all out of the picture with faster shutter, or allow some of it in with slower shutter - our choice. The TTL flash is still automatic exposure either way, and not affected by shutter speed.
The camera does have Slow Sync and/or Rear Curtain Sync settings, which will use the metered slow 1/4 second, or whatever the ambient actually metered. In these sync modes, the shutter speed will NOT increase to 1/60 second. This is special use however, NOT for normal flash pictures.
There are several ifs and buts, but flash is where the fun is, and it's not hard (but we do have to use our heads to think about it). If you are going to get into flash much, you need a bigger hot shoe flash, specifically one that will do bounce flash, which is a great thing, makes a huge difference.