Two images of a dot in a half-silvered glass sphere

[Anoonumos]

Hi,
http://imageshack.us/photo/my-images/141/optica.png/

The sphere in the picture is made of glass with n = 1.60.
The curved side of this sphere is a mirror. The question is why we see two images of the black dot.

Homework Equations

Snells law?

The Attempt at a Solution

One image is created directly by the mirror (1/f = 1/s0 + 1/s1), but I don't know what causes the other image. I don't think the object is one of the images, because we have to calculate the distance to the image (distance object is already given), and i haven't used n = 1.60 in that case. Any ideas?

 

[technician]

You are on the right track with an image created by the mirror. This is formed by light traveling to the right from the dot and hitting the curved surface.
What about light traveling to the LEFT from the dot, it meets the flat glass surface and is refracted...check REAL and APPARENT depth

 

[Anoonumos]

Well, we're looking at the dot with a zero degree angle, so there wouldn't be any refraction right? I guess the mirror refracts some light as well, which could explain a second image. Thank you for your response.

 

[technician]

You have to be very careful here. You usually associate refraction with a change in angle and you are used to seeing diagrams with light changing direction as it enters or leaves glass blocks. It is more than this
You need to realize that all of this occurs because light CHANGES SPEED as it passes from air into glass. It is slower in glass than it is in air (1.5 x slower). This means that objects in glass (or water) appear to be closer than they really are due to refraction.
A swimming pool looks shallow for this reason and points in glass look closer than they really are for the same reason.
Look at real and apparent depth in your physics textbook for the explanation and the diagrams.

 

[Anoonumos]

I see, thanks. One final question just to check: the other image would be affected by this as well right? (Image created by mirror looks closer) and both images would be virtual.

 

[technician]

Yes. The reflected rays from the curved surface will be refracted when they come out of the glass so this image is not exactly the same as if the curved surface did not have glass in front.

 

[Anoonumos]

I've calculated the distance from the image created by the mirror to the mirror. It is to the right side of the mirror. Let's call the distance x.
I now want to calculate the distance to the flat side of the sphere. I think I should use: (1/n * R) + x, because that image is not in glass anymore. Am I correct? Or should I use (1/n) * (R + x) ?

Now I think about it again, I think it should actually be the second one: (1/n) * (R + x)