The attached figure is from the lab manual Prelab Question 1 at the end of the w

Question

The attached figure is from the lab manual Prelab Question 1 at the end of the writeup. Although it will not be graded, perform the derivation described there anyway. When looking down from nearly straight overhead which of the following are true:
1. Only the object is visible.
2. Only the image is visible.
3. Both the object and the image are visible.
4. The image point I is at h'=h/n
5. The image point I is at h'=n h


image available here. #3 :http://www.cramster.com/answers-jul-10/physics/refractive-index-easy-multiple-due-1-hour-help2-law-reflection_884873.aspx?rec=0

Explanation / Answer

In this case only image is visible which results in smaller apparent depth. The formula for the apparent depth and real depth is:

h/h' = n2/n1.

Since n1 = 1 and n2 = n, in present case, h/h' = n
or the image point is at :

h' = h/n.

Thus options 2 & 4 are correct.

Derivation:

From Snell's law,

n1Sin1 = n2Sin2

For small angles, Sin = Tan and given that n1 = 1 and n2 = n

Thus n = Tan1/Tan2

but Tan1 = x/h' and Tan2 = x/h

So n = h/h'

or h' = h/n

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