
optisch
visual
Relating to the outer appearance; visual. It describes how something looks.
Optisch macht das neue Handy einen sehr guten Eindruck.
Visually, the new phone makes a very good impression.
visual / optical
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visual
Relating to the outer appearance; visual. It describes how something looks.
Optisch macht das neue Handy einen sehr guten Eindruck.
Visually, the new phone makes a very good impression.

optical
Relating to seeing, perception with the eyes, or the science of light (optics).
Eine optische Täuschung spielt mit der Wahrnehmung unseres Gehirns.
An optical illusion plays with the perception of our brain.
The adjective 'optisch' (visual/optical) is directly connected with the noun 'die Optik' (optics/appearance). 'Die Optik' refers both to the appearance of something and to the scientific study of light.
Die Optik dieses neuen Autos gefällt mir sehr gut.
I really like the look of this new car.
When 'optisch' (visual) describes general appearance, it is about aesthetics. When it refers to seeing itself or to technical devices, it is about the function of the eye or physics.
Optisch ist die Wohnung sehr schön, aber sie ist unpraktisch.
Visually, the apartment is very nice, but it is impractical.
In the meaning 'relating to appearance', 'optisch' (visually) is often used like an adverb at the beginning or in the middle of a sentence to comment on the whole sentence or on an adjective.
Optisch hat sich hier in den letzten Jahren viel verändert.
Visually, a lot has changed here in recent years.
In the technical or scientific meaning, 'optisch' (optical) often appears with certain nouns. A very common and important collocation is 'optische Täuschung' (optical illusion).
Die Linien auf dem Bild scheinen krumm zu sein, aber das ist nur eine optische Täuschung.
The lines in the picture seem to be crooked, but that is only an optical illusion.
external / outward
Both words can describe the appearance of something without referring to its function. optisch particularly emphasizes the visible effect or impression, while äußerlich contrasts the outside with the inside or the essence. optisch is usually the better fit for a purely visual effect, while äußerlich is more suitable when contrasting the outside with the inside.

Die neue Farbe verändert das Fahrrad optisch, aber nicht seine Funktion.
The new color changes the bicycle's appearance, but not its function.
Die neue Farbe verändert das Fahrrad äußerlich, aber nicht seine Funktion.
The new color changes the bicycle's outward appearance, but not its function.