I've been reading some Murakami and came across 反射(する) and 映る。I've never given them much thought other than that they mean reflection but I was wondering if there's some subtle nuance that I'm not aware of.
Their uses are different, and they are not interchangeable.
映る is an intransitive verb that means "(for an image) to be reflected/projected (on a mirror/screen/wall/etc)". The subject must be a recognizable "image", and the mirror/screen-like object is marked with に. You can also say テレビに映る. The transitive equivalent is 映す.
反射する is both transitive and intransitive. When used transitively, the subject is a mirror-like object, and the object is usually a light/radio/sound wave, and sometimes something abstract like "damage". There doesn't have to be an "image".
- (as a game item description) この盾はダメージの20%を相手に反射する。
When 反射する is used intransitively, the subject is a light/sound/radio wave.
Finally, 反射 can be used only for physical phenomenons. You have to use 反映 for a sentence like "the price reflects the demand". 反射/反映 does not mean "to think back deeply", either.
Not a native speaker, but since Korean has similar words (both the Sino-Korean word 反射-hada and a native word bichida similar to 映る), probably it is the same in Japanese. The following is same for Korean.
反射 is the literal action of reflecting something. It can be used for visuals, but is not limited to. For example, it can be used for sound, or even some abstract effects. 映る is an action of something is being reflected on some surface, so that the image can be seen by people. It is only used for visuals, unless it is used metaphorically.
And since 反射 is from Chinese, I think it is often more formal than the native words like 映る or bichida.