Image formed by a plane-concave lens and a concave mirror

In summary, the problem involves an observer looking at an object through a plane-convex lens of radius 20 cm and refraction index 1.5. There is also a concave mirror of radius 30 cm located 40 cm behind the lens. The object is placed at the same distance from both the lens and the mirror. Two images are formed by the optical system, with the first image having a distance of -13.33 cm and a height of -1.33 cm, and the second image having a distance of 40 cm and a height of -12 cm. The equations used to solve for the images are 1/s + 1/s' = (n_2/n_1 - 1)(
  • #1
lorele
5
0

Homework Statement


An observer looks at an object of height 2 cm through a plane-convex lens of radius 20 cm and refraction index 1.5. There's a concave mirror of radius 30 cm 40 cm behind it, and the object is at the same distance of both the lens and the mirror. Find the images formed by the optical system and draw the diagram.
Solutions:
Image 1: s'=-13,3 cm; y'=-1.33 cm
Image 2: s'=40 cm; y'=-12 cm

Homework Equations



[itex]1/s + 1/s=(n_2/n_1 -1)(1/R_1-1/R_2)[/itex]
[itex]1/s + 1/s'=1/f[/itex][/B]

The Attempt at a Solution


[/B]
For the first image: [itex]\frac{1}{-20} + \frac{1}{-s'}=\frac{1}{2}(\frac{1}{\infty}-\frac{1}{-20}) \implies s'=-13,33 cm[/itex]
This is correct (one question: why do I have to use "-s'"? Shouldn't the result give the correct sign using s'?).
But I can't get the diagram to agree with this result. Could anyone make one?

And then, for the second image, using the first image as an object:
s=26,67, f=R/2=15 cm. s'=34 cm
Using the first object:
s=20 cm, f=15 cm. s'=60 cm.
In this case, both possible values are wrong. I think the problem derives from my incapacity to picture the diagram. Could it be that I have to account for the divergence of light caused by the first lens to calculate the position of the image created by the mirror? And how do I do that?
 
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  • #2
Try sketching the diagram. There are three images.
I can never remember the sign conventions so I rely on sketching to get the placement right. If the diagram disagrees with the calculation, then the calculation is usualky in error.
 

Related to Image formed by a plane-concave lens and a concave mirror

1. What is the difference between the image formed by a plane-concave lens and a concave mirror?

The image formed by a plane-concave lens is virtual, upright, and diminished, while the image formed by a concave mirror is real, inverted, and can be either magnified or diminished depending on the distance of the object from the mirror.

2. How does the focal length of a plane-concave lens and a concave mirror affect the image formed?

The focal length of a plane-concave lens determines the size and position of the virtual image, while the focal length of a concave mirror determines the size and position of the real image.

3. Can a plane-concave lens and a concave mirror form both real and virtual images?

Yes, both a plane-concave lens and a concave mirror can form both real and virtual images, depending on the position of the object relative to the lens or mirror.

4. How does the curvature of a plane-concave lens and a concave mirror affect the image formed?

The curvature of a plane-concave lens affects the magnification and clarity of the virtual image, while the curvature of a concave mirror affects the magnification and distortion of the real image.

5. What factors determine the size and position of the image formed by a plane-concave lens and a concave mirror?

The size and position of the image formed by a plane-concave lens and a concave mirror are determined by the focal length, curvature, and distance between the object and the lens or mirror.

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