Can I measure refraction of light in centimeters?

You can't measure an angle with a linear ruler. There is no such thing as a metric angle. Measure angles with a protractor which reads in degrees or whatever its calibration is.

You CAN measure a trig function of an angle with a ruler. Let the angle to be measured be one of the angles of a right triangle. Measure the length of 2 of the sides of the triangle and use the lengths to compute the sine, cosine, or tangent of the angle. Since Snell's law normally involves the sine of the angle of refraction, it would make sense to divide the side opposite the angle by the hypotenuse; this would give the sine of the angle directly. BTW, when doing this you can use any kind of ruler available; the division cancels the units, whether they be cm, in, pica, etc.....

Keep up the good work......

Well MEmily (clever name), when you ask a question like this, the person reading it has to make some assumptions. It seems like you were sending something like a laser beam or maybe a white light through some kind of transparent container and then you measured how much the beam moved from either the x or y axis depending on which way the container was placed.

You always measured from the same point where the light came out of the container.

Is that the way it worked?

The vinegar is a little surprising. I would not have thought it would refract that much, but depending on exactly how you were told to do this and what you measured from, I would guess that you did pretty well. Veggy oil is certainly going to make a bigger difference than water, and if that is so than vinigar should be between them.

No, angles aren't measured in cm. That's a length.

It's possible this represents one side of a triangle, and if you know another side you could use trigonometry to get the angle. But these are not angles.

What happens in refraction is that a ray coming in at one angle is bent to another angle. The other angle will depend on the medium. What you were supposed to do probably involved measuring both the incoming and outgoing angles. So you are also missing any information about the angle that the light hit the surface at.

angles are measured in degrees not cm. you should be using a protractor to find the angles. are the refractions just being represented on paper?