Week 11 (Nov. 4 - 8)
Read: Reflection of Light Waves (Chap. 15); Opacity, transparency, and Snell's law (Chap. 16);, Atmospheric refraction (Chap. 17),
PHY 202 Lecture: Wave optics
PHY 202 Lecture: Wave optics
Quiz: Monday.
Homework:
No class on Wednesday (I'll be out of town)
Lab: This week, we will be building and characterizing a Keplerian Telescope. This type of telescope involves two lenses: an eyepiece lens (the one you put your eye next to) and an objective lens (the one nearest the object you are viewing). To build the telescope, you will need a light source, an optical rail, carriages and lens mounts, lenses, a screen, and a partially frosted microscope slide.
First, place the light source on one side of the laboratory. This will act as a “star”. On the opposite side of the laboratory, aim your optical rail at the star. Now place a lens (having a focal length of approximately 40 cm) in a lens holder atop the optical rail. This will serve as our objective lens. It will probably be a good idea to mount the objective lens about in the middle of the rail.
On the side of the lens opposite the star, place a small rigid white screen. Move the screen forward or backwards until an image of the star is focused on the screen. The image may be quite small. The distance between the lens and the screen is called the image distance, since the object distance is very far, the image distance should be approximately equal to the focal length of the lens.
Incidentally, this image is called a ``real image," as opposed to a ``virtual image"; a virtual image is one formed at an apparent location at which no light rays are actually converging—for instance the image formed behind a mirror.
Carefully inspect the real image on the screen. Is it inverted or upright? Is it larger or smaller than the actual objects being observed? Calculate the magnification of your optical setup thus far. You might notice that how big the image looks to you depends on how close you put your eye to the image itself: when you are near the image, it appears large; when distant, it appears small. This is because when it is near, the image takes up a larger portion of your field of view. Technically speaking, the image occupies a larger solid angle.
You can try to make the image of the star that appears on the screen larger by moving your eye very close to it. Try this. How close can you get your eye before it looks blurry? This distance is called your ``near point”. Your near point is set by the ability of the ciliary muscles of your eye to squeeze the lens in your eye so as to focus light on the retina in the rear of your eye.
This physiological limitation can be overcome by using a magnifying glass to inspect the image on the screen formed by the objective lens. When you use a magnifying glass to inspect the image, the image itself acts as the object for the magnifying glass, which in turn projects an image onto your retina. Now: select a lens having a focal length of about 10 cm. We will call this magnifying glass our eyepiece lens.
Inspect the image on the screen with your eyepiece lens. What problems do you encounter when trying to look through the eyepiece lens at the screen? It would probably be much easier to inspect the image from behind the screen; this way your head will not block the light from the star. Unfortunately, the screen is opaque. Let's now replace the screen with a semi-transparent sheet of glass, such as a partially frosted microscope slide.
Again, focus the image of the star on the frosted glass using your objective lens. Now mount your eyepiece lens in a holder on the side of the frosted glass opposite the objective lens. Move the eyepiece lens until you can look through it and see a focused image of the star on the frosted glass slide. How is the distance between the image and the eyepiece related to the focal length of the eyepiece lens? In particular, is the distance from the frosted slide to the eyepiece lens larger or smaller than the focal length of the eyepiece lens? (It should be slightly smaller.) You might need to do a quick measurement to figure out the focal length of your eyepiece lens to be sure.
Now remove the frosted glass slide. Can you still use your telescope to view distant star? Does this surprise you?
Congratulations! You have now built a Keplerian telescope. Try to use your telescope to observe distant objects, such as shapes drawn on a board on the opposite side of the laboratory.
What is the magnification of your telescope? In order to determine the magnification, use the method described by Galileo. Galileo observed two objects simultaneously, one through the telescope and the other with the unaided eye. This is a bit tricky, but give it a try. Have your lab partner draw a small square (about an inch across) on the chalkboard and look at it through your telescope from the other side of the room. It will look magnified when viewed through the scope.
Now, have your lab partner stand next to the small square on the chalk board. While looking with one eye through the scope, look through the other eye past the lenses. Have your lab partner try to draw a second square on the chalk board that looks to you to be the same size as the magnified square. Again, this may be a bit tricky. If successful, you can use the ratio of the sizes of these two squares to determine the magnification of your telescope. Does the approximate formula (Magnification) = (objective focal length) / (eyepiece focal length) work?
A Keplerian telescope is an example of a refracting telescope. We are going to try to understand how this telescope works using semi-quantitative ray diagrams. As mentioned before, a Keplerian telescope uses two lenses, an objective and an eyepiece. Light from a distant object first passes through the objective lens. The objective lens forms a real inverted image which is somewhat smaller than the object itself. Sketch this optical arrangement in your lab book. The image produced by the objective then acts as the object for the eyepiece. In a refracting telescope, the image produced by the objective lies at, or just inside, the focal point of the eyepiece lens. Add this to your sketch. If the focal length of the eyepiece is much less than the user’s near point, then he or she can use the eyepiece as a magnifying glass to inspect this image up close without straining his or her eye. What is the relationship between the focal lengths of the objective and eyepiece lenses and the total length of your telescope? What is the relationship between the focal lengths of the two lenses and the magnification of your telescope? Why is this the case? Draw diagrams and try to understand how your telescope works. For a bit of the theory, here is a short video:
Chapter 15 (2 videos):
Check out the following link to an applet designed by Walter Fendt. It clearly illustrates the reflection and refraction of light waves using Huygens' Principle
Chapter 16 (2 videos):
Chapter 17 (1 videos):
Homework:
- Snell's law from wave refraction (ex. 16.1)
- Snell's law from fermat's principle (Ex. 16.2*)
- Spherical mirrors and the thin-lens equation (Ex. 12.7*).
No class on Wednesday (I'll be out of town)
Lab: This week, we will be building and characterizing a Keplerian Telescope. This type of telescope involves two lenses: an eyepiece lens (the one you put your eye next to) and an objective lens (the one nearest the object you are viewing). To build the telescope, you will need a light source, an optical rail, carriages and lens mounts, lenses, a screen, and a partially frosted microscope slide.
First, place the light source on one side of the laboratory. This will act as a “star”. On the opposite side of the laboratory, aim your optical rail at the star. Now place a lens (having a focal length of approximately 40 cm) in a lens holder atop the optical rail. This will serve as our objective lens. It will probably be a good idea to mount the objective lens about in the middle of the rail.
On the side of the lens opposite the star, place a small rigid white screen. Move the screen forward or backwards until an image of the star is focused on the screen. The image may be quite small. The distance between the lens and the screen is called the image distance, since the object distance is very far, the image distance should be approximately equal to the focal length of the lens.
Incidentally, this image is called a ``real image," as opposed to a ``virtual image"; a virtual image is one formed at an apparent location at which no light rays are actually converging—for instance the image formed behind a mirror.
Carefully inspect the real image on the screen. Is it inverted or upright? Is it larger or smaller than the actual objects being observed? Calculate the magnification of your optical setup thus far. You might notice that how big the image looks to you depends on how close you put your eye to the image itself: when you are near the image, it appears large; when distant, it appears small. This is because when it is near, the image takes up a larger portion of your field of view. Technically speaking, the image occupies a larger solid angle.
You can try to make the image of the star that appears on the screen larger by moving your eye very close to it. Try this. How close can you get your eye before it looks blurry? This distance is called your ``near point”. Your near point is set by the ability of the ciliary muscles of your eye to squeeze the lens in your eye so as to focus light on the retina in the rear of your eye.
This physiological limitation can be overcome by using a magnifying glass to inspect the image on the screen formed by the objective lens. When you use a magnifying glass to inspect the image, the image itself acts as the object for the magnifying glass, which in turn projects an image onto your retina. Now: select a lens having a focal length of about 10 cm. We will call this magnifying glass our eyepiece lens.
Inspect the image on the screen with your eyepiece lens. What problems do you encounter when trying to look through the eyepiece lens at the screen? It would probably be much easier to inspect the image from behind the screen; this way your head will not block the light from the star. Unfortunately, the screen is opaque. Let's now replace the screen with a semi-transparent sheet of glass, such as a partially frosted microscope slide.
Again, focus the image of the star on the frosted glass using your objective lens. Now mount your eyepiece lens in a holder on the side of the frosted glass opposite the objective lens. Move the eyepiece lens until you can look through it and see a focused image of the star on the frosted glass slide. How is the distance between the image and the eyepiece related to the focal length of the eyepiece lens? In particular, is the distance from the frosted slide to the eyepiece lens larger or smaller than the focal length of the eyepiece lens? (It should be slightly smaller.) You might need to do a quick measurement to figure out the focal length of your eyepiece lens to be sure.
Now remove the frosted glass slide. Can you still use your telescope to view distant star? Does this surprise you?
Congratulations! You have now built a Keplerian telescope. Try to use your telescope to observe distant objects, such as shapes drawn on a board on the opposite side of the laboratory.
What is the magnification of your telescope? In order to determine the magnification, use the method described by Galileo. Galileo observed two objects simultaneously, one through the telescope and the other with the unaided eye. This is a bit tricky, but give it a try. Have your lab partner draw a small square (about an inch across) on the chalkboard and look at it through your telescope from the other side of the room. It will look magnified when viewed through the scope.
Now, have your lab partner stand next to the small square on the chalk board. While looking with one eye through the scope, look through the other eye past the lenses. Have your lab partner try to draw a second square on the chalk board that looks to you to be the same size as the magnified square. Again, this may be a bit tricky. If successful, you can use the ratio of the sizes of these two squares to determine the magnification of your telescope. Does the approximate formula (Magnification) = (objective focal length) / (eyepiece focal length) work?
A Keplerian telescope is an example of a refracting telescope. We are going to try to understand how this telescope works using semi-quantitative ray diagrams. As mentioned before, a Keplerian telescope uses two lenses, an objective and an eyepiece. Light from a distant object first passes through the objective lens. The objective lens forms a real inverted image which is somewhat smaller than the object itself. Sketch this optical arrangement in your lab book. The image produced by the objective then acts as the object for the eyepiece. In a refracting telescope, the image produced by the objective lies at, or just inside, the focal point of the eyepiece lens. Add this to your sketch. If the focal length of the eyepiece is much less than the user’s near point, then he or she can use the eyepiece as a magnifying glass to inspect this image up close without straining his or her eye. What is the relationship between the focal lengths of the objective and eyepiece lenses and the total length of your telescope? What is the relationship between the focal lengths of the two lenses and the magnification of your telescope? Why is this the case? Draw diagrams and try to understand how your telescope works. For a bit of the theory, here is a short video:
Chapter 15 (2 videos):
Check out the following link to an applet designed by Walter Fendt. It clearly illustrates the reflection and refraction of light waves using Huygens' Principle
Chapter 16 (2 videos):
Chapter 17 (1 videos):