A few figurative artists, such as Caravaggio in his brilliant painting of Narcissus (1594-96), have used reflections to great effect. Generally, though, they’re the preserve of the landscape artist. Given a suitable body of still water, what more appropriate addition to any great view than its reflection.

Albrecht Dürer was one of the first landscape painters to recognise their importance, and to take the time and care to get them right, in his View of Innsbruck from about 1495.

Over a hundred and fifty years later, Nicolas Poussin used them to add to the placid atmosphere in his idealised Landscape with a Calm (c 1651). As shown in the detail below, the upper parts of the Italianate mansion, together with the livestock on the far bank of the lake, are painstakingly reflected on the lake’s surface, telling the viewer that there isn’t a breath of breeze to bring ripples to disturb the reflection.

The optics of reflections are surprisingly complex, and many careful and accurate landscape painters have strayed from their geometry on occasion.

While JMW Turner wasn’t above making the odd mistake, he was normally accurate, as seen in the complex reflections of Pope’s Villa, at Twickenham from 1808. Most of his oil paintings, such as those of Venice, adhere to optical principles.

While more typical of his late and much looser style, Turner remains accurate in this freely interpreted view of Campo Santo, Venice from 1842, where reflected sails are prominent and angelic in appearance.

Some of his watercolours, such as Norham Castle, on the River Tweed (1823), have quirks in their reflections: for example, the reflection appears to show another high point at the left edge of the castle which isn’t matched by an equivalent high point in the original.

Among the French Impressionists, it was Claude Monet who was most skilled in the use and detail of reflections.

Monet’s masterwork Autumn on the Seine, Argenteuil from 1873 is an excellent example with finely broken and rippled reflections.

Although not all the paintings in Monet’s series of poplars include reflections, where they do they add to their overall effect, as seen in Poplars on the Bank of the Epte, Autumn (1891).

Alfred Sisley made good use of reflections in this view of Moret Bridge in the Sunlight from 1892, one of a series of over ten similar views of the town of Moret-sur-Loing, where he lived his later years.

Meticulous reflections are a hallmark of some of Enrique Simonet’s late landscapes, including Reflections on the River which he painted between 1918-23.

Landscape painters have also used reflections of complex subjects in innovative ways. One technique, as seen in Simonet’s painting above, is to show the subject mainly or exclusively in reflection.

In 1899, Gustav Klimt holidayed with the Flöge family in the popular resort of Golling, where he painted Tranquil Pond, also known as A Morning by the Pond, or Egelsee near Golling, Salzburg (1899). This places its emphasis on the reflections rather than their originals, which are cropped by the top of his canvas.

Alder Trunks from 1893 is one of Laurits Andersen Ring’s finest landscapes, and earned it place in the Danish Royal Collection. In common with Klimt, Ring shows these old coppiced alders mainly in reflection. Although its details are quite painterly, the overall effect is still strongly realist.

Throughout his long career, reflections painted by Paul Cézanne have departed from the traditional.

This is one of Cézanne’s best-known paintings, showing a view across Lake Annecy from Talloires and featuring the distinctive Château de Duingt and the foothills which rise behind it. The water surface is shown to cover almost the entire lower half of the painting, within which the reflections of the castle are central and dominant features.

Comparison with views of the actual motif reveals that Cézanne has brought the far shore considerably closer to the viewer than it really is, by enlarging all the objects on that shore. Measurement on modern satellite images shows the distance to be 0.76 km or just under half a mile, but here it looks much closer.

Although some have questioned whether the lake surface is ever calm enough to permit such clear reflections, there is photographic evidence that, on occasion, the reflections can be as clear as those depicted here. However neither that nor optical principles suggest that the reflections could possibly appear the way that Cézanne has painted them.

Ferdinand Hodler also intentionally manipulated reflections to serve his greater purpose.

This reached an extreme in Hodler’s Parallelist landscapes, among which his Rhythmic Landscape on Lake Geneva (1908) is most unusual for its treatment of reflections on the surface of the lake. In those the gaps in the train of cumulus clouds become dark blue pillars, which are optically impossible, but generate much of the rhythm in the lower half of the painting.