Refractive index using a traveling microscope

[Manasan3010]

For finding refractive index of a glass block, we use n=real-depth / apparent-depth
For calculating apparent depth microscope is raised vertically until a clear focus is obtained of the underlying mark beneath the glass blob. Given that microscope is perpendicular to the mark, Wouldn't the apparent depth equal to real depth like in the case of looking under a pond/water container from directly above(Image - 3)
What am I missing here?

 

[Jeff Root]

I know that the image viewed through glass, even perpendicularly, is
raised above where it would be without the glass, by the refraction.
But I don't know enough about it to fully answer the question.

However, I have questions of my own about the diagram labeled
"Real and apparent thickness".

What is supposed to be going on at the top of the scale, marked "S"?
The first scale has a squared-off top, the second scale has a blank space
and a black horizontal oval at the top, while the third scale has no blank
space but the black oval becomes vertical. Suggesting an exaggerated
and rather crudely-drawn change in viewing angle of a circle, such as the
field of the microscope. But I see no reason for that to be shown at the
top of the scale, even if that is what it is supposed to be.

The first and second microscopes have squared-off tops, while the third
has an extension with a rounded top. What is that about?

I take it that "V" is a vernier scale. Why are the index marks on the first
vernier scale closer together than those on the second and third? Just
crude drawing technique?

What is "M"? Why is the second one different from the first and third?
Is it because the microscope is correctly positioned to focus on the thing
to be observed, while the first microscope is focussed on the base and the
third microscope is focussed on the top surface?

I suspect that it would have been helpful to include the text accompanying
the diagram. The diagram labled "Fig.12.1.3" is very clear without needing
any verbal explanation, given the knowledge of what phenomenon it is
demonstrating.

-- Jeff, in Minneapolis

 

[Andy Resnick]

What am I missing here?

I think you are missing the concept of 'optical thickness' d/n, where d is the physical thickness of the upper block and n the refractive index. The objective lens moves d/n to re-focus, so you can determine n directly.

 

[sophiecentaur]

Wouldn't the apparent depth equal to real depth like in the case of looking under a pond/water container from directly above(Image - 3)
What am I missing here?

This is not correct. The apparent depth of water gets less away from the vertical (a consequence of the Sine functions in Snell's Law) but for normal incidence, it's still less than the real depth according to the reactive index. Apparent depth can only be found by some change in angle (however small) for light entering different parts of the pupil (and the focussing of the microscope). The two boys are necessary in that diagram because the angles for the boy directly above are too small to show on the diagram. Most ray diagrams, demonstrating how lenses etc. work, use massive diagrammatic eyes so that the subtended angles are 20 degrees or more. That gives a wrong impression as well as the right basic message.