Circle in the Sky

Classical Mechanics Level 1

The image below is a photograph of the surface of the ocean taken from underwater. We see a bright circle in the center with a dark outside. Which of the following best explains this?

Light from outside the circle is bent away by the water as it enters and doesn’t reach the diver The bright circle is the sun, which is magnified as light reflects off the water There are clouds in the sky above the surface, creating a bright circle surrounded by shadow The camera has a limited field of view and intensifies reflected light underwater

6 solutions

Danielle Scarano Staff
Dec 19, 2017

Light that hits the water is refracted at the surface according to the law of refraction ( Snell's Law ). The air above the surface has a different index of refraction than the ocean. This results in the appearance of a compressed view of the surface above—appearing as a circle of light. The dark region surrounding the circle displays totally internally reflected light from underwater. Since there is little light below the surface in deep water, it appears dark to observers.

But refraction doesnt happen in a certain area. Refraction happen on all the sea surface. So you shouldnt see the circle. You are seeing circle because of the camera's lens. Camera's lens acts as an angle limitter.

Erdem Metin - 3 years, 5 months ago

That followed my line of tought as well. The "correct" answer surprised me, perhaps it's the wording (-:

Mark van der Velden - 3 years, 5 months ago

I chose this answer as well, as a photographer, It seemed that the wide angle of the lens has the corners of the image looking more horizontally through the water, instead of up through the surface. The vignetting being off-center raised flags to me.

Alexander Osbourn - 3 years, 5 months ago

After thinking about it, the "correct" answer is correct. Refraction does happen on all the sea surface, but to an observer it comes in at different angles so it doesn't result in exactly the same effect across the field of view. Due to refraction, light from above water that you see underwater actually comes from a wider angle than it appears underwater. At some point, the angle coming from above water will "cut off" (exceed 90 degrees) so you will cease to get light from above water, resulting in the dark region. It results in a circular region because the angle only depends on how far something is radially, the direction does not matter based on the position of the observer.

You can also confirm that it is not due to the camera's lens by googling images of pictures taken underwater, where you can see the cutting off into darkness but it doesn't fit the circular shape of the lens at all.

Forest Yang - 3 years, 5 months ago

really? bc when i look up at a depth beneath the surface, i dont see this circle. only when taken with a ccd. the camera is to blame

Adam Fletcher - 3 years, 5 months ago

You might be in a shallow pool, the floor would be brightly lit, so instead of seeing dark you would be seeing the floor of the pool and it would be difficult to find the circle. This circle is actually formed and can be seen with the eye as well as a camera.

You can test this by stretching your hand out enough just below the surface of the water. Your hand will be outside the circle, and you would be able to see its reflection on the water-air boundary.

Pranshu Gaba - 3 years, 5 months ago

Qwerty Uiop
Dec 26, 2017

I was able to eliminate the incorrect solutions by considering the view from the bottom of a pool on a sunny day, when I am not facing the sun.

Corentin Gitton
Dec 29, 2017

I find the correct answer confusing and thus I eliminated the others. The "Entering light" is indeed refracted, but I don't see how the "Entering light" can be reflected "from below". To me the dark area is just the limit at which "Entering light" cannot be refracted in such a way that it reaches the camera lens with the given angle. (Because of the law of refraction)

Stewart Gordon
Dec 29, 2017

To elaborate on the existing explanations:

This is an effect known as Snell's window. The water surface acts as a lens, refracting the entire hemisphere of the view above the water into the camera via the bright area we see. The circle will get bigger the deeper down you go. The refractive index of water is around $\frac43$ , giving a critical angle (the limit of the angle of refraction as the angle of incidence approaches $90^\circ$ ) of about $49^\circ$ . As such, the light we see from above lies within a $49^\circ$ radius of the vertical line through the camera. Outside this radius, no direct light from above the water reaches the camera. (At least, this would be the case if the water were perfectly level - in reality the waves create some irregularity.)

Abhinav Singh
Dec 25, 2017

Light that enters into the water is refracted as the refractive index on water is more than that of air above it so when the light bents it makes a circle of light as seen here.

Aaghaz Mahajan
May 16, 2018

All based on Critical Angle.......

Circle in the Sky

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