Understanding how exposures work doesn't require a physics degree... it simply requires a desire to learn. If you follow a recipe in a cook-book that calls for 1 cup of milk, you probably wouldn't argue that understanding how to use the marks on the side of the measure cup to fill the cup to the correct amount is complicated. But if you've never seen a measuring cup before you your life, it might be helpful if someone pointed out why it has marks on the side.
Understanding exposure is roughly about as complicated as understanding how to use a measuring cup.
In simple terms the amount of light outside is considerably more than the amount of light inside.
You can't do much about the amount of light outside... the Sun is lighting that up and we can't control the Sun.
We CAN, however, control the light inside the house. We can either add more light until the amount of light inside is not so much dimmer than the amount of light outside (and this would be a more traditional approach before the age of digital photography) -OR- we can take advantage of the fact that computers can merge the data from two or more images to create one final image. HDR (high dynamic range) is a fancy name for a simple idea... shoot the exposure as if you only care about how well the exposure looks outside the window -- and don't care about the interior. Then shoot another exposure as if you only care about the interior look -- and don't care about the look out the window.
Now imagine you could take a pair of scissors and cut out the "windows" from the first picture and tape them onto the windows in the second exposure... so you have a nicely exposed interior AND a nicely exposed exterior.
You don't need scissors. The computer will do it for you.
The Canon T4i has a built-in HDR mode (in fact, it has two of them). It will work best if you use a tripod that way the scene in all the images will precisely align. HDR software can compensate for some movement (but it has to crop the images) and if you don't have a tripod I am told the "nighttime" HDR mode works a bit better (it's better about aligning the images.)
Here are two examples. This first example is the more traditional method .... I exposed for the light through the window (ignoring the interior) but I used a flash to boost the light on the interior. I did not want the interior to be as bright as the outside light (otherwise it wont look natural) so I told the camera to slightly de-power the flash. I think I shot this using "-1" to the "Flash Exposure Compensation" control (FEC). Again, I wanted this to be a bit dark... I could have changed the flash power to brighten it up.
This is a blacksmith's shop:
This next example uses the HDR technique. This is actually the in-camera HDR from my Canon EOS 5D Mark IV. Take a look at the windows on the right side of the room and you can see the outside isn't over-exposed -- but would have been in a normal single image.
BTW, this happens to be the upstairs floor of Thomas Edison's Menlo Park lab.
So two options:
1). Boost interior light to more closely match the outdoor light (usually allowing the interior to be slightly darker) and...
2). Use HDR by taking multiple exposures and merge them using either in-camera HDR or computer software.
Several programs have the ability to do HDR processing (including Photoshop). A program called "PhotoMatix" is purpose-built just to do HDR, it's very good, very easy to use, and many people feel that it also produces some of the best results (it can do anything from a "natural" look... to highly surreal results (more artsy and less natural).
