Why aren't the distances of the images the same in this problem?

[jaumzaum]

I was solving the below question

"An object is 30 cm above a container filled up with water. The lower end of the container is coated silver and acts like an ideal spherical concave mirror of radius 60cm. Find the distance of the image to the surface of water."

http://img856.imageshack.us/img856/5575/sadgsdfg.png

If I find first find the image 1 made by the plan dioptre and than the image 2 that the image 1 makes with the mirror, I find 104cm (that is the correct answer)

But if I find first the image 3 that the mirror makes with the object (considering all in air) and THAN the image 4 that the image 3 does when going to water, I find 137cm.

Why the answers aren't the same? Shouldn't they be by the reversibility of light principle?

 

[Doc Al]

If I find first find the image 1 made by the plan dioptre and than the image 2 that the image 1 makes with the mirror, I find 104cm (that is the correct answer)

I understand how you got the 104 cm answer. You considered the refraction at the air/water interface and then the reflection in the mirror.

But I don't understand the rest of what you did. The principle of reversibility tells you that if you now put a source of light at that spot, the image will end up at the original location above the water line. Which is true. Show your work so we can see what you did.

 

[jaumzaum]

I understand how you got the 104 cm answer. You considered the refraction at the air/water interface and then the reflection in the mirror.

But I don't understand the rest of what you did. The principle of reversibility tells you that if you now put a source of light at that spot, the image will end up at the original location above the water line. Which is true. Show your work so we can see what you did.

Hi Doc,

If I consider first the reflection:

1/30 = 1/170 + 1/s'

s' = 255/7cm => 140-255/7 = 725/7 cm under the surface

Now the refraction in the air /water surface

s'' = -725/7.4/3 = -138cm (138 cm under the surface)

Why the results are not the same?

 

[Doc Al]

Hi Doc,

If I consider first the reflection:

1/30 = 1/170 + 1/s'

Where did the 170 come from? The 'source' is now 104 cm under the water surface.

 

[jaumzaum]

Where did the 170 come from? The 'source' is now 104 cm under the water surface.

Thanks Doc, now that I thought better the way I'm following is not explained for the pronciple of reversibility :)

But anyway, I wanted to consider first the reflection and than the refraction (the 170 comes from the original distrance of the object to the mirror). I don't know why but for me the results should be the same. I thought that the order the things happenned were not important for the final result.So in a problem like this we should first consider the things that actually happened in first place and than the things that happenned after?

 

[Doc Al]

Thanks Doc, now that I thought better the way I'm following is not explained for the pronciple of reversibility :)

OK. I suspected I didn't understand you.

But anyway, I wanted to consider first the reflection and than the refraction (the 170 comes from the original distrance of the object to the mirror). I don't know why but for me the results should be the same. I thought that the order the things happenned were not important for the final result.So in a problem like this we should first consider the things that actually happened in first place and than the things that happenned after?

I would treat things in the order that the light meets them. Here the light first meets the air/water interface, them meets the mirror. (I see no reason why the answer would make sense if you mixed up the order of things.)

 

[jaumzaum]

OK. I suspected I didn't understand you.

I would treat things in the order that the light meets them. Here the light first meets the air/water interface, them meets the mirror. (I see no reason why the answer would make sense if you mixed up the order of things.)

Thanks Doc, now I've got it
I thought that I could mix up the order and get the same answer (I don't know why I thought it too) :)

[]'s
John