Which ray diagram is correct for a Compound microscope?

[Wrichik Basu]

Here are two ray diagrams for compound microscope, the first one proposed by the book, and the second one recommended by the teacher:

In the first image, the light rays form a real image A'B', which becomes the virtual object for the eyepiece. See, the original rays are carried forward to the eyepiece, which then form a virtual image, A"B".

In the second image, when the real image A'B' is formed, new rays start from it, and end up forming the virtual image A''B".

I feel the second one is wrong, because new rays cannot start from a real image, but the original rays should go forth and get refracted again to form the virtual image.

What is your opinion? Which diagram is correct?

 

[mjc123]

Both are correct, but the top one is perhaps clearer as to what is physically happening, as it carries the same rays from object to eye. However, rays are in fact coming from the real image A'B' in many directions (not just the two shown in the top picture), and it is quite legitimate to select the two shown in the bottom picture if that illustrates the formation of the virtual image more clearly. (Those rays of course do not originate at A'B', but come from the object AB, just like the others - though you might need a lens bigger than O to draw them.)

 

[Andy Resnick]

What is your opinion? Which diagram is correct?

Both diagrams are 'correct' (meaning they both correctly locate the virtual image), but the second diagram is more in the spirit of ray tracing. For example, in the upper diagram, the refraction of the rays in the eyepiece is (seemingly) arbitrary, while the corresponding rays in the lower diagram obey clear rules.

I would interpret the lower diagram in terms of sequential imaging by the lenses: the objective lens forms an image which is the object for the eyepiece.

Does that help?

 

[ZapperZ]

What is your opinion? Which diagram is correct?

The whole point of ray tracing is that you can draw, to scale, the optics and then, using some simple rules, get the final image. One of the simple rules is that a ray parallel to the principle axis entering a lens, will be deflected so that it will pass through the focal point on the other side. The ray that goes straight through the center of the lens, will not be deflected. So simply by drawing straight lines, and looking at where these rays cross each other on the other side of the lens, you get an image, both the location and the size.

So following such rules, you know how the rays get bent (or not bent) when they pass through the lens. These deflections are not made arbitrarily.

But if you look at your second figure, you'll see that for the rays that passed through the eye piece, it appears that there were no set rules on how the rays were deflected:

How would you know to what angle these should change? The deflection of the rays appears to be arbitrary. There seems to be no rules on how to continue with the drawing.

Compare that to the first diagram, where the IMAGE now is the OBJECT for the eye piece, and the same ray tracing rules are reapplied to it with the eye piece. There's nothing arbitrary in the ray lines here.

Zz.

 

[Wrichik Basu]

@mjc123, @Andy Resnick and @ZapperZ thanks for your detailed explanations.

 

[Master Om]

Here are two ray diagrams for compound microscope, the first one proposed by the book, and the second one recommended by the teacher:

View attachment 232683

View attachment 232684

In the first image, the light rays form a real image A'B', which becomes the virtual object for the eyepiece. See, the original rays are carried forward to the eyepiece, which then form a virtual image, A"B".

In the second image, when the real image A'B' is formed, new rays start from it, and end up forming the virtual image A''B".

I feel the second one is wrong, because new rays cannot start from a real image, but the original rays should go forth and get refracted again to form the virtual image.

What is your opinion? Which diagram is correct?

The first diagram is drawn using using SYSTEM RAYS where as 2ND one is drawn using TRACING RAYS .
If my purpose is to find the final image 2nd one is easy way to find considering every lens independent and drawing images to the image point only. But if I am going to explain how they rays pass through the lens SYSTEM and forms an image 1st one is the only correct Ray diagram
Hence it depends what you are explaining . If working of compound microscope is explained then 1st is the diagram. It's better to draw 3 rays (one passing through focus to be precise ) which may pass parallel and finally through the focus of eye piece.
Hence right or wrong depends on the context.

 

[Master Om]

The whole point of ray tracing is that you can draw, to scale, the optics and then, using some simple rules, get the final image. One of the simple rules is that a ray parallel to the principle axis entering a lens, will be deflected so that it will pass through the focal point on the other side. The ray that goes straight through the center of the lens, will not be deflected. So simply by drawing straight lines, and looking at where these rays cross each other on the other side of the lens, you get an image, both the location and the size.

So following such rules, you know how the rays get bent (or not bent) when they pass through the lens. These deflections are not made arbitrarily.

But if you look at your second figure, you'll see that for the rays that passed through the eye piece, it appears that there were no set rules on how the rays were deflected:
View attachment 232706
How would you know to what angle these should change? The deflection of the rays appears to be arbitrary. There seems to be no rules on how to continue with the drawing.

Compare that to the first diagram, where the IMAGE now is the OBJECT for the eye piece, and the same ray tracing rules are reapplied to it with the eye piece. There's nothing arbitrary in the ray lines here.

Zz.

Actually arbitrary is the second diagram as it considers the lenses independently. If I am explaining how the microscope works I have to show how rays pass from object to final image and showing it bending at top of 2nd image is wrong with that context.
Also what u said that there were no rules how rays deflected is also wrong . They rays bend with respect to image formed. The position of final image decides how the rays bend at the lenses so that it will form an image infront of the eye. Hence drawing another Ray through the focus makes it clear . Both diagrams are in sprit of Ray tracing . But the second one does not explain HOW RAYS PASS IN A COMPOUND MICROSCOPE. Use the Wolfram alpha demonstration project software to see how image is formed.
https://demonstrations.wolfram.com/RayDiagramsForMicroscopeAndTelescope/

 

[sophiecentaur]

I feel the second one is wrong, because new rays cannot start from a real image, but the original rays should go forth and get refracted again to form the virtual image.

This is something that confuses many people. It's like one of those tricks that are used by the teachers in Algebra, Geometry and Calculus etc. and we all say to ourselves "Why did he do that?" But it's actually OK and valid.
The point is that, if a real image has been formed then light from it will follow all the right rules - just the same as if it were an actual object. A virtual image that's been formed from a real object will be there, whichever rays you choose. The lens calculations can be transferred from real intermediate mage to a 'pretend' real intermediate object.
Why do it that way? Well, if you were to draw the ray diagram to scale, the angles would all be such that your lines would be so fat and they would lay over each other, preventing any visible pattern. A,B and A',B' could be drawn ) small enough that the Eyepiece would intercept the actual rays from the initial object and everything would be legit and hunky dory. Except that the diagram would be difficult to make sense of.

More Problems:
If you want enough light from the Object to get into your eye, the diameters of the two lenses need to be suitable and the so-called Exit Pupil needs to be at least as big as your eye pupil or the image you see will be dim. Also, the way the object is illuminated needs to be right so that enough light from the lamp actually finds its way into your eye.

 

[jtbell]

It might be a useful exercise to "complete" the second diagram, by extending the rays that apparently start at the intermediate image, backwards to the object via the first lens, and by extending the rays that apparently end at the intermediate image, forwards to the eye through the second lens (thereby showing that they help to form the final virtual image in this case).

The principal rays that the second diagram shows are merely tools for locating images purely geometrically. There is nothing special about them otherwise. You can alternatively locate the intermediate and final images purely by calculation, using the thin-lens equation $$\frac 1 {d_o} + \frac 1 {d_i} = \frac 1 f$$ and the magnification equation $$\frac {h_i} {h_o} = - \frac {d_i} {d_o} = M$$ and then draw an infinite number of rays through the system, using the object, intermediate image and final image points as "anchors."

All this ignores the presence of entrance and exit stops and pupils as mentioned by @sophiecentaur. If you know where these are, and how big they are, you can use them to see which of these rays actually make it all the way through the system.

 

[sophiecentaur]

It might be a useful exercise to "complete" the second diagram, by extending the rays that apparently start at the intermediate image, backwards to the object via the first lens, and by extending the rays that apparently end at the intermediate image, forwards to the eye through the second lens (thereby showing that they help to form the final virtual image in this case).

I would agree except that it would be such a bind to do those constructions and calculations. Much easier to use the two conventional virtual rays - one parallel to the axis and one through the centre of the lens; no sums involved. I prefer to believe that something works until I really really need to get inside. Life can be too short and, in any case, you don't get spherical lenses in real life so it's all very theoretical.

As for stops and pupils - they are quite a major leap in complexity. There is a lot of vignetting in cheap camera lenses because you need so much more (expensive ED) glass and it also implies getting the curvatures of the lenses to be correct over a bigger area.

Optical equipment (especially top-end amateur) is like a game of top trumps which the retailers play with great skill at the expense of their vulnerable customers. (Ditto hifi, cars, tools etc, etc.)