Why The Pond Appears Shallower - and some thoughts on Feynman
"Refraction of light - it bends away from normal when entering air from water - so..." This line of statements backed up by (variants of) the same picture appears in most basic explanations of this phenomenon.
What is often glossed over is that light bending away from normal on entering air obviously explains ONLY that the virtual image of an underwater object (including the pond bed) gets laterally shifted but NOT the image appearing LIFTED vertically. In elementary explanations, one 'cheats' in the picture by continuing the refracted ray back into water ONLY up to a point that lies vertically above the actual object. This begs the question: Why is the ray continued back into water only that much?
As for the rod dipped in water appearing bent, one may note that the rod appears bent at only the interface between air and water; the portion in water is STRAIGHT.
Feynman has answered much of the question in his Chapter 27, Vol I of his famous lectures. He derives from Fermat's principle of least time the result that the ratio between real depth and apparent depth is equal to the refractive index of the medium, when the surface of separation is a plane. This explains the 'image getting elevated'. One could add that, observationally, whatever be the ANGLE at which the line joining the observer and the virtual image (the refracted ray) emerges from the refracting surface, this ratio between real and apparent depth holds (otherwise, the rod dipped in water will not only be bent at the interface, the part within water will also be CURVED). I have not entirely been able to convince myself that this angle independence also is contained in Feynman's explanation (basically I have not yet spent adequate time contemplating what the Master has said). One intuitive way of saying it could be: "refraction lifts up everything by a constant ratio of the depth at which it lies. Then once this lifting is over, it does not matter from where in the air you look at it, you see the same lifted image; and the position of the image does not depend on where it is viewed from in any case, even in the case of a plane mirror".
Maybe that is all there is to it (somehow some doubt lingers!). One needs only to be precise about what an image is and calculate how refraction causes a virtual image and then things settle. Perhaps the 'elementary way' of explaining things has caused confusion when getting to the heart of the matter...
Winding up that 'stream of consciousness', I would like to add here that the flower of the Indian Physics community is NOT unanimous in its opinion of Feynman lectures. Along with fervent assertions that they 'surely rank among the classics of our times', the lectures also have invited (sometimes round) condemnations for (allegedly) misleading students by creating an illusive, lazily intuitive picture of physics, by hiding nitti-grities in glib talk and intellectual sleights of hand. 'Dont think you can do things the way Feynman does. He is a genius; you are not!' is a very common way of rebuking young votaries of Feynman.
What is often glossed over is that light bending away from normal on entering air obviously explains ONLY that the virtual image of an underwater object (including the pond bed) gets laterally shifted but NOT the image appearing LIFTED vertically. In elementary explanations, one 'cheats' in the picture by continuing the refracted ray back into water ONLY up to a point that lies vertically above the actual object. This begs the question: Why is the ray continued back into water only that much?
As for the rod dipped in water appearing bent, one may note that the rod appears bent at only the interface between air and water; the portion in water is STRAIGHT.
Feynman has answered much of the question in his Chapter 27, Vol I of his famous lectures. He derives from Fermat's principle of least time the result that the ratio between real depth and apparent depth is equal to the refractive index of the medium, when the surface of separation is a plane. This explains the 'image getting elevated'. One could add that, observationally, whatever be the ANGLE at which the line joining the observer and the virtual image (the refracted ray) emerges from the refracting surface, this ratio between real and apparent depth holds (otherwise, the rod dipped in water will not only be bent at the interface, the part within water will also be CURVED). I have not entirely been able to convince myself that this angle independence also is contained in Feynman's explanation (basically I have not yet spent adequate time contemplating what the Master has said). One intuitive way of saying it could be: "refraction lifts up everything by a constant ratio of the depth at which it lies. Then once this lifting is over, it does not matter from where in the air you look at it, you see the same lifted image; and the position of the image does not depend on where it is viewed from in any case, even in the case of a plane mirror".
Maybe that is all there is to it (somehow some doubt lingers!). One needs only to be precise about what an image is and calculate how refraction causes a virtual image and then things settle. Perhaps the 'elementary way' of explaining things has caused confusion when getting to the heart of the matter...
Winding up that 'stream of consciousness', I would like to add here that the flower of the Indian Physics community is NOT unanimous in its opinion of Feynman lectures. Along with fervent assertions that they 'surely rank among the classics of our times', the lectures also have invited (sometimes round) condemnations for (allegedly) misleading students by creating an illusive, lazily intuitive picture of physics, by hiding nitti-grities in glib talk and intellectual sleights of hand. 'Dont think you can do things the way Feynman does. He is a genius; you are not!' is a very common way of rebuking young votaries of Feynman.
posted by R.Nandakumar @ 11:11 PM
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