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# The Physics of ....Staring at Shadows?

Updated: May 9, 2022

The ever-ingenious Rory Geoghegan forwarded the image to me here a few days ago. It's a pretty straightforward image of strong shadows on a wall, but Rory had noticed an oddity....

Rory takes it form there...

The photograph is unusual for the following reasons:

1. The shadows of leaves and twigs etc. are quite sharp considering that the objects themselves were 9 metres away. The Sun is not a point source; its angular size in the sky is 0.5°. A twig that is 1 cm in diameter will have a blurred shadow at a distance of just 1 metre, with little umbra; beyond 1.1 metres it will have no umbra because its angular size would then be less than 0.5°.

2. The shadows are larger that the objects.

In ordinary sunlight the shadows are the same size as the objects causing them, if we neglect the blurred edges.

In this instance the shadows are over 50% larger than the objects. (35 cm:23 cm)

Explanation

The light source is the reflection of the Sun in the windscreen of a car. If the windscreen were flat then the Sun’s image would appear to be ‘at infinity’ and have parallel rays.

However, the reflection from the convex surface of the car’s windscreen seems to come from a point approximately half the radius of curvature below the surface. Windscreens do not normally have a uniform radius of curvature; they are usually more curved at the sides. A typical minimum radius of curvature is about one metre. So the apparent image of the Sun would be about 0.5 metre or more below the surface and would appear to be almost a point source (<1’ of arc in this case).

In this case the ratio of shadow to object was 35 cm: 23 cm, i.e. about 1.5. The object to shadow distance was 9 m. So, the car was approximately 18 metres from the object (the railing).

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