Optics-Optical Instruments Lab

Instructor Outline: Optics-Optical Instruments

UM Physics Demo Lab 07/2013

Lab length: 70 minutes

Lab objective: To instruct the students about optical instruments formed from multiple optical elements: periscopes, compound microscopes, refracting telescopes and reflecting telescopes.

Materials

Yard stick periscope mirror mount

2 51 mm square flat mirrors

Refracting telescope kit – objective, eyepiece, foam cylinder, cardboard ring in red plastic cylinder, two cardboard tubes

Microscope stand — three magnetic thumb tacks + ½” steel washer

5 ¼” diameter cosmetic mirror on stand (concave/flat)

3 1/4” diameter cosmetic mirror on stand (concave/flat)

Hand-held magnifying glass

40 W “candle” lamp

Power strip

Calculator

Clear plastic rulers

Meter stick

Business card

Micro Fiber cloth for polishing mirrors and lenses

Exploration: 25 minutes - Group Lab Work

The students assemble a simple periscope from two plane mirrors and produce a ray tracing diagram illustrating how the optical path of the periscope is based on the law of equal angles for reflection from a plane mirror.

Next, the students measure the focal length, f/number and diopter magnification of the eyepiece from the refracting telescope. Next, they use the eyepiece of the telescope as a simple magnifier and observe a magnified virtual, upright image for a printed page which is at an object distance less than the focal length. This is review from the previous lab. They then calculate the magnification for the simple magnifier as M=25 cm/f. Next they place the eyepiece on a stand which puts the printed page just outside the focal length of the lens, now the objective of a compound microscope. They observe that the image is now inverted (and hence real) and produce a compound microscope by viewing the image from the objective through the hand magnifier, which functions as a low-power eyepiece. They can also use the small inset magnifier as a high-power eyepiece. Next they measure the focal length of the refracting telescope objective lens and predict what they will see if they view a distant object with the combined objective/eyepiece assembled as a telescope. They then view distant objects and calculate the angular magnification of the refracting telescope as:

– (objective focal Length)/ (eyepiece focal length)

Analysis: 5 minutes – Lecture

Real and virtual images formation by a thin converging lens are reviewed from the previous lab. The optical paths for the compound microscope and telescope are reviewed. Dispersion is demonstrated with a prism as motivation for making telescopes with mirrors instead of lenses to avoid chromatic aberration.

Exploration: 15 minutes – Group Lab Work

The students next investigate the properties of a spherical mirror, demonstrating that it brings parallel light from infinity to a single focus. They then demonstrate that a lamp placed at the focus will be projected as an image at infinity, the same as for a lamp placed at the focus of converging thin lens. They deduce that a light house beacon can be made with a concave mirror as well as a converging lens

Analysis: 5 minutes – Lecture

The thin lens equation is reviewed and shown to be valid for the converging concave spherical mirror, the only difference being that the image and object distances are positive on same side of the mirror, rather than on opposite sides as for the thin lens. The relationship between focal length and radius of curvature f = R/2 is introduced.

Application: 15 minutes – Group Lab Work

The students are lead to suggest a design for a reflecting telescope which uses a plane mirror to direct the real image outside of the beam of the primary mirror. They then construct this telescope using two cosmetic mirrors (5 ¼” spherical, 3 ¼” flat) and the hand magnifier as a low power eyepiece. They draw a ray tracing diagram for the optical path of the reflecting telescope they have built.

Analysis: 5 minutes – Lecture

The Newtonian reflecting telescope optical path is reviewed and Newton-Cassegrain and Schmidt-camera optical paths are also discussed.

Suggested Demos:

Astronomical type Newtonian reflecting telescope

Concepts developed:

1. The Law of Reflection states that the angle of reflection is equal to the angle of incidence for a reflected ray of light. The angles are defined with respect to the direction perpendicular to the reflecting surface called the normal.

2. Images where the light actually emanates from the location of the image are called real images. Images where the light only appears to emanate from the image location but does not actually do so are called virtual images. The image of a lamp filament projected by a thin converging lens is real. The image in a plane mirror is virtual.

3. Two plane mirrors can be combined to form a simple periscope which allows the user to view images of objects from around a corner or below an obstruction.

4. If an object is placed inside the focal length of a thin converging lens, an upright magnified virtual image is observed. The angular magnification for the simple magnifier can be calculated as 25 cm/f.

5. If an object is placed just outside the focal length of a lens (called the objective) a real, inverted image is formed. Viewing this real image inside the focal length of a second simple magnifier (called the eyepiece) produces a magnified virtual image which remains inverted. This combination of two lenses is called a compound microscope. Short focal length objectives and eyepieces produce the greatest magnification.

6. Viewing the inverted real image formed by a long focal length objective lens with a second simple magnifier (eyepiece) produces a refracting telescope. As with the compound microscope, the final image is inverted and magnified. The magnification for this telescope is easily calculated as –fobjective/ feyepiece where the minus sign indicates that the overall image is inverted. Long focal length objectives and short focal length eyepieces produce the highest magnifications at the price of a narrow field of view.

7. For a compound microscope, the object to be viewed is placed outside but very close to the focal point of the objective lens. For the refracting telescope, the object to be observed is very far away (“at infinity”). For a compound microscope, the highest magnification is achieved when both the objective and the eyepiece have short focal lengths (high diopter magnifications). By contrast, the highest magnifications for a refracting telescope are achieved with a long focal length (low diopter magnification) objective lens and a short focal length (high diopter magnification) eyepiece.

8. Light passing through a refractive medium such as glass is separated into its component colors, as demonstrated by the rainbow of colors that emerges when white light falls on a glass prism or water droplets, forming a rainbow. This phenomenon, called dispersion, is undesirable in a telescope requiring special coatings on the lenses to correct it. When dispersion is present in lenses it is called chromatic aberration—“color distortion”.

9. Concave mirrors with a spherical shape will focus parallel rays of light to a focal point in the same manner as a thin converging lens, this time on the same side of the mirror as the object. The focal length of the mirror is easy to calculate as ½ the radius of curvature of the mirror: f=1/2 R.

10. One method to reduce chromatic aberration and the absorption of light passing through a telescope is to use a focusing (concave) mirror for an objective rather than a lens. The most basic of these designs is called a Newtonian reflecting telescope in honor of its inventor, Isaac Newton.

11. A concave spherical mirror does not perfectly focus parallel rays to a single point. Rather, rays near the edge of the mirror focus shorter than those near the axis of the mirror (paraxial rays). This distorts the resulting image and is called spherical aberration. Thick lenses made with spherical surfaces also exhibit spherical aberration, giving rise to the “fish eye” distortion seen when using the lens as a magnifier.

12. Spherical aberration can be eliminated from the images formed by mirrors and lenses by using a parabolic shape for the curved surfaces, but parabolic surfaces are much harder to produce.

13. A thin corrective lens can also be used to correct telescopes for spherical aberration, allowing large, easy to produce spherical mirrors to produce sharp images. This technique produces a telescope called a “Schmidt Camera” in honor of the 19th century optician who developed the prescription for the corrective lens and successfully produced telescopes of this design.

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