Convex Lenses: Determining Real/Virtual Images

[marla1]

Homework Statement

Two thin convex lenses (1 and 2) and a small object are arranged as shown.

a) Use the three principal rays to determine the location of the image of the object produced by lens 1.
. Object
--------.F1---0(Thin lens 1)---.F1-----------.F2----0(Thin lens 2 - longer)---->F2-----------

b) Treat the image produced by lens 1 as an object for lens 2. Use the three principal rays to determine the location of the image of this object produced by lens 2.
Is this image produced by the pair of lenses real or virtual? Explain your reasoning.

c) Repeat parts a and b for the case in which lens 2 is replaced with a different lens (lens 3), as shown below.
.Object
----.F1--0(Thin lens 1)---.F1---.F3-------0(Thin lens 3 - longer)-------.F3------------------------

Is the image produced by the pair of lenses real or virtual? Explain your reasoning.

Homework Equations

Not quite sure of the relevant equations here.

The Attempt at a Solution

For part a, I would draw a parallelogram of principal rays and the location of the image object would be inbetween F1 and F2?

For part b, the location of the image object produced by lens 2 would be towards the right end of the page. It would be a real image.

For part c, I am unsure how my answer would differ from above, although I think it would be a virtual image.

Thanks in advance for your help! Better pictures are attached.

 

[Mandeep Deka]

First of all, what is the condition for a real or a virtual image to be formed?

 

[marla1]

A real image is a representation of an object (source) in which the perceived location is actually a point of convergence of the rays of light that make up the image. If a screen is placed in the plane of a real image the image will generally become visible on the screen.

A virtual image is an image in which the outgoing rays from a point on the object always diverge.

 

[Mandeep Deka]

Exactly..
and for a convex lens, a virtual image is formed only when the object is placed between the lens and its focus.
Now after refraction from the first lens, where will the image be formed?
Remember, this image can behave as an object, because formation of a real image is actually the convergence of rays at a point. But after convergence the rays will continue to move in their own directions, thus making that point of convergence equivalent to a point source of light!

The basic essence of the solution to your problem is simple..
If the point where the rays converge after refraction through the first lens, don't lie beyond the focus of the second lens the final image will be real but if the point of convergence of rays after first refraction lies beyond the focus of the second lens, the image will be virtual.

 

[rwisz]

I would like to point out that the answer to this question may vary depending on the specific details of the lenses and object used. However, I will provide a general response based on the given information.

a) Using the three principal rays, we can determine the location of the image produced by lens 1. The first ray, parallel to the principal axis, will pass through the focal point on the other side of the lens. The second ray, passing through the center of the lens, will not change direction. The third ray, passing through the focal point, will emerge parallel to the principal axis. The intersection of these three rays will determine the location of the image object.

b) Treating the image produced by lens 1 as an object for lens 2, we can use the same three principal rays to determine the location of the final image produced by the pair of lenses. The image produced by lens 1 will act as a virtual object for lens 2, and the final image will be located on the same side of lens 2 as the original object. The image produced by this pair of lenses will be real, as the rays converge to a point on the opposite side of the lenses.

c) Repeating the same process with lens 3, we can determine the location of the final image produced by the pair of lenses. However, the image produced by lens 3 will act as a real object for lens 2. Depending on the specific details of lens 3, the final image may be real or virtual. If lens 3 is a converging lens (thicker in the middle), the final image will be real. If lens 3 is a diverging lens (thinner in the middle), the final image will be virtual.

In conclusion, the location and nature of the final image produced by a pair of convex lenses will depend on the specific details of the lenses used. It is important to consider the focal lengths and thickness of the lenses in order to determine the location and nature of the final image.