Physics - optics - apparent depth

[preet]

My physics textbook has a diagram that illustrates Apparent Depth... but I can't understand it.

Specifically, why does the image appear where it is (at apparent depth)? I understand that as the light from the object moves from water to air, refraction occurs... but I'm thinking, shouldn't the angle at which the person's eyes receive the light go all the way to the bottom of the pool or something? It seems as if the light is still reaching the person's eyes the same horizontal distance from the object? Is that true?

So then, is the the following image true for when the light will bend towards the normal, where the end of the yellow line to the top of the surface will be apparent depth? (would explain increased apparent depth)...

TiA.

 

[ShawnD]

My physics textbook has a diagram that illustrates Apparent Depth... but I can't understand it.

Specifically, why does the image appear where it is (at apparent depth)? I understand that as the light from the object moves from water to air, refraction occurs... but I'm thinking, shouldn't the angle at which the person's eyes receive the light go all the way to the bottom of the pool or something? It seems as if the light is still reaching the person's eyes the same horizontal distance from the object? Is that true?

To make it easier to see, I've redrawn the picture with the lines more spread out.
http://www3.telus.net/public/darich1/science/refract_beholder.jpg

The pink line shows where you think the light is going. The blue line shows where the light really is going. If you put a ruler to your screen, and your resolution is 1024x768, you'll notice that both blue and pink lines starting from the water level are about 2.5 inches in length; that means light is reflected from an object that is 2.5 inches from where the light touches the water. The difference of perception comes from the angle. Your brain thinks the light travels in a straight line, so the pink line continues at the same angle as the angle of incidence.

 

[maverick280857]

Its simply that light moving from a rarer to a denser medium bends towards the normal and (as a result) light moving from a denser to a rarer medium bends away from the normal. As the speed of light in the medium can be qualitatively considered to describe its "optical density" we have $$c_{water} < c_{air}$$.

Now if an object is located at a depth below the free surface of water, light rays traveling from it when refracted at the water-air interface are refracted (as you have correctly analyzed). But any such light ray (except the one that passes normally and undeviated) bends away from the normal. When such a light ray reaches the eye and forms an image, we are naturally inclined to retrace it back to where it (apparently) comes from and regard that place as the object that is forming the image. The terms real and apparent depth can be expressed as mathematical quantities which are related to the relative refractive index of the medium (in this case that of water wrt air).

Yes indeed from the diagram it is clear that the retraced object is on the same vertical line as the original object. However, the incident ray and the emergent ray are different.

In the latter diagram therefore, the fish that is below is the object and the one above is the retraced object. So its better if you draw the lower fish in the pond itself

Hope that helps...

Cheers
Vivek

 

[maverick280857]

ShawnD that's a brilliant representation. Three cheers for the brain

 

[janmorez]

Hi I also have difficulty understanding as to why the point is the result of an intersection of a vertical line from the bottom point and the extended dotted line of the refracted beam (well I get that, I just don't get where that vertical line comes from). I read the thread but there's an image missing in ShawnD's post.

Also sorry for bumping an old thread...