Optics question: light reflecting off a colored surface

[PotentialE]

From my understanding, when white light hits a surface, all of the frequencies within the white light are absorbed except one, which is reflected, and that is the color of the object. For instance, a blue plastic appears blue because it absorbs all frequencies except that of blue.
Why then, can certain materials, colored plastics in particular, reflect images in color. Images reflected in plastic are not as vivid as a mirror, but they are in color nonetheless.
Why if a material can show a reflection is it not just a different color? For instance, I can see by looking at the back of my phone case, blue plastic, that the shirt I'm wearing is red. If the case can reflect red, why isn't the case itself just red? What properties of material or light allow reflections to be seen over other colors?

 

[Simon Bridge]

From my understanding, when white light hits a surface, all of the frequencies within the white light are absorbed except one, which is reflected, and that is the color of the object. For instance, a blue plastic appears blue because it absorbs all frequencies except that of blue.

That's what we tell the kiddies - next level up: different materials absorb different combinations of wavelengths. The color you see is how your eye responds to the wavelengths that get scattered.

Why then, can certain materials, colored plastics in particular, reflect images in color. Images reflected in plastic are not as vivid as a mirror, but they are in color nonetheless.

There is more than one thing happening. Materials only absorb a proportion of the incident light. Light that gets scattered gives the diffuse color but you also get specular effects and straight reflection as of a mirror. In general, incident light can be absorbed, scattered, reflected, or transmitted.

Why if a material can show a reflection is it not just a different color? For instance, I can see by looking at the back of my phone case, blue plastic, that the shirt I'm wearing is red. If the case can reflect red, why isn't the case itself just red? What properties of material or light allow reflections to be seen over other colors?

In the case of the blue surface - it is reflecting visible light of many wavelengths, but some of the wavelengths are absorbed, scattering blue light.

What you see is the combination of lots of processes - the scatter/reflection gets some help from the image processing in your brain too... so the red shirt probably looks redder than the reflected red light would indicate because your brain knows your shirt is supposed to be red.

Similarly, when you look at differently colored objects under monochromatic light it sometimes looks like you can see the colors there anyway.