spiegeln
to reflect
To reflect an image or light on a smooth surface, as a mirror does.
Die ruhige Wasseroberfläche des Sees spiegelt die Berge perfekt.
The calm surface of the lake reflects the mountains perfectly.

to reflect / mirror
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to reflect
To reflect an image or light on a smooth surface, as a mirror does.
Die ruhige Wasseroberfläche des Sees spiegelt die Berge perfekt.
The calm surface of the lake reflects the mountains perfectly.

The verb 'spiegeln' (to reflect/mirror) is derived directly from the noun 'der Spiegel' (the mirror). When something 'spiegelt' (reflects), it functions like a mirror.
In einem sauberen Löffel kann man sich auch spiegeln.
You can also see yourself reflected in a clean spoon.
'Spiegeln' (to reflect/mirror) can be used transitively or reflexively, which changes the sentence structure. Either a surface reflects something (accusative object), or something is reflected in a surface (reflexive pronoun).
Das Fenster spiegelt die Wolken am Himmel.
The window reflects the clouds in the sky.
When a person or object is reflected, the reflective surface is almost always indicated with the preposition 'in' followed by the dative.
Sie spiegelte sich kurz in der Fensterscheibe des Busses.
She briefly saw herself reflected in the bus window.
In the figurative meaning, 'spiegeln' (to reflect) is often used with abstract nouns. Typical combinations are that something reflects feelings, an opinion, a state, or reality.
Seine leeren Augen spiegelten seine tiefe Traurigkeit.
His empty eyes reflected his deep sadness.
to represent / portray / constitute
'darstellen' and 'spiegeln' can both mean that something shows content or a situation. 'darstellen' is more active and direct: a text, image, or chart deliberately shows something or describes it. 'spiegeln', in a figurative sense, means that something makes something else recognizable or reflects it. It often sounds as if a condition, opinion, or mood becomes visible in something. Learners may confuse the words because both have to do with 'zeigen' (to show). 'darstellen' fits better when something is explained or depicted deliberately; 'spiegeln' fits better when something is a reflection of something else.

Die vielen Fragen spiegeln die Unsicherheit im Team.
The many questions reflect the uncertainty in the team.
Die Tabelle stellt die Kosten der letzten drei Monate dar.
The table shows the costs from the last three months.