University of Toronto Edward S. Rogers Sr. Department of Electrical and Computer Engineering

ECE318 – Fundamentals of Optics

Lab #1 SPHERICAL LENSES AND OPTICAL INSTRUMENTS

CAUTION: ● NEVER TOUCH THE SURFACES OF OPTICAL ELEMENTS. ● HOLD A LENS BY TOUCHING ONLY ITS EDGE.

Apparatus:

• Optical rail • Halogen table lamp • White viewing screen • One-meter ruler • A scale with arrowhead (to be used as object) • Convex lens C (unknown focal length) • Concave lens D (unknown focal length) • Concave mirror (unknown focal length and radius) • Three convex lenses with known focal lengths (f = 10 cm or 34 cm)

Reference: Class notes and “Introduction to Optics” Chapter 21, by Pedrotti, 3rd edition. PART I: THIN LENSES AND MIRRORS Background:

Lenses Lenses are transparent optical devices that refract light in a way such that an image of the source of light is formed. When parallel rays impinge on a converging (convex) lens, they rays are refracted such that they come together at a focal point (F). The distance between the lens and the focal point is called the focal length (f). An imaginary line parallel to the light rays and through the center of the lens is called the principal axis. On the other hand, when parallel rays impinge on a diverging (concave) lens, they are spread out by the lens. The focus of diverging lens is on the same side of the lens as the incident parallel rays.

Fig. 1 Focal point of lenses

The location of the image created by a lens can be determined graphically via the following:

1. A ray parallel to the principal axis will pass through the focal point of the lens. 2. A ray through the focal point of the lens will emerge parallel to the principal axis

upon exit from the lens.

Fig. 2 Graphical construction of image position for a lens

Depending on the location of the object and the focal length of the lens, an image may form on the same side of the lens as that of the object. This is called a virtual image, which does not form a visible projection on a viewing screen but can be imaged by eye or camera when looking back through the lens.

Fig. 3 Virtual images created by lens

If a lens has thickness that is negligible compared to its focal length, it can be called “thin lens” and its image location can be determined by the lensmaker’s equation:

ho

hi

do

di

1𝑑#+1𝑑%=1𝑓(1)

where f is the focal length, and do and di are the object and image distance respectively.

Moreover, the magnification power of the lens, i.e. the ratio between the height of the image and the height of the object, is given by:

𝑀 =ℎ%ℎ#= −

𝑑%𝑑#(2)

The following sign conventions are used when working with thin lens and the equations above:

• f is positive (negative) for a converging (diverging) lens. • do is positive (negative) when the object is to the left (right) of the lens. • di is positive (negative) for an image formed to the right (left) of the lens. • m is positive if the image is upright with respect to the object and negative if the

image is inverted with respect to the object.

Mirrors Mirrors are opaque optical devices that reflect light in a way such that an image of the source of light is formed. The ray tracing rules for the lens can also be applied to determine the image location for a mirror. More specifically, the radius of curvature of a spherical mirror twice its focal length.

Fig. 4 Graphical construction of image position for a mirror

Procedure: In part I, you will learn a few common methods used to determine the focal length of thin lenses and the radius of curvature of spherical mirrors. Ray diagrams should be drawn for each experiment performed and the results should be checked by calculation where applicable. (1) Convex Lens We will use three different methods to determine the focal length of the convex lens C. Make sure all the components are of the same height before you begin. Method (1)

1. Illuminate the object using the halogen lamp. 2. Place one of the convex lens with known focal length behind the object to serve as

the collimator (how?), followed by convex lens C. 3. Place the viewing screen such that a clear and sharp image can be observed. 4. Obtain the focal length of lens C by measuring the distance between the lens and

the screen. Method (2)

1. Remove the collimator. 2. Move lens C slowly along the optical rail, from very close to far away from the

object (i.e. change the object distance from less than focal length to larger than twice the focal length). Observe how the screen needs to be moved accordingly in order to capture an image.

3. Select an arrangement of lens C and the viewing screen such that a sharp image is observed.

Fig 5. Image that is in focus and sharp

4. Measure the object and image distances as well as the object and image sizes. Note

the orientation of the image. 5. Calculate the focal length of lens C using equation (1).

6. Calculate the magnification using equation (2) and compare with direct measurement.

Method (3)

1. Place a second convex lens of known focal length near the object such that a virtual image is created.

2. Using this virtual image as the object, place convex lens C in a position such that a real image can be formed.

3. From the object and image distances involved and the known focal length of the second lens, find the focal length of convex lens C.

Compare the result obtained using the three different methods and comment on your results. (2) Concave Lens Find the focal length of the concave lens D using method (3) that was used to measure the focal length of convex lens C. (3) Concave Mirror

1. Place the concave mirror onto the optical rail behind the object. Slightly tilt the mirror slightly away from the optical rail axis such that the image formed by the mirror reflection can be capture using a screen that is on the same side as the object.

Fig. 6 Set-up for measuring the radius of curvature of the concave mirror

2. Arrange the mirror and the screen such that a sharp image is observed. Record the object and image distances. Change the location of the concave mirror and repeat the measurement. Calculate the average value for the radius of curvature and the focal length of the mirror.

3. Find the unique arrangement that places the image in the same plane as the object.

This indicates the radius of curvature of the mirror directly. PART II: OPTICAL INSTRUMENTS Background: Optical instruments such as microscope and telescope can be constructed via a system of lenses. In a system with multiple lenses, the lensmaker’s equation can be applied to find the image location for the first lens, which then serve as the object location such that the equation can be applied for the second lens. The process is repeated all for the lenses. The total magnification of the optical instrument is the product of the magnifications of the individual lenses. The compound microscope uses a combination of objective lens and eyepiece to produce a highly magnified image of an object that is 25.4 cm (D) from the eye piece. The magnifying power is given by:

𝑀 = −𝑑%#/0

𝑑##/0

𝐷𝑑#232 (3)

where do

eye ≈ fe is the object distance of the eyepiece and doobj and di

obj are the object and image distance of the objective lens respectively.

. Fig. 7 Optical set-up of a compound microscope

The telescope objective lens produces a small image of a distant object. It is adjusted such that that the final image is at infinity so that the eye is completely relaxed when viewing it. The magnification of a telescope is given by:

𝑀 =𝑓#𝑓2(4)

Fig. 8 Optical set-up of a telescope Procedure: (1) Compound microscope

1. Set up the lamp and the illuminated scale as the object. Place the white viewing screen between the lamp and the scale to dim the light.

CAUTION: the very bright halogen light may hurt your eyes if you look at it directly or look at object through the microscope without the white viewing screen.

2. Set up the microscope using the appropriate lenses. You must justify your choice

of lenses.

3. Look from towards the object through your compound microscope. Describe the image that you see.

4. Measure the appropriate optical distances to determine the magnifying power.

5. Measure the magnifying power by direct comparison of the image size with the

scale held at the near point (D). (2) Telescope

1. Use the lamp source, the scale, and appropriate lenses to create an object that is effectively at infinity (hint: a collimator is required).

2. Set up an astronomical telescope using lenses of appropriate focal length for the objective and the eyepiece. Place a white view screen between the lamp and the collimator before you look toward the object.

CAUTION: the very bright halogen light may hurt your eyes if you look at it directly or look at object through the microscope without the white viewing screen.

3. Adjust the eyepiece location to obtain a sharp image. Describe the quality of the

image and compare with what you observed directly from the collimator.

4. Calculate the magnification power of the telescope.

5. Using an additional lens to convert the astronomical telescope to a terrestrial telescope. Calculate its magnification power and compare with the astronomical telescope. Compare the size (i.e. length) of the two types of telescopes.

Bonus: What the approximate location of the eye relative to the eyepiece in order for you to observe the full field of view of the image?

Appendix: Optics Cleaning Procedure CAUTION: The cleaning process should be supervised by a TA! CAUTION: Always wear gloves before cleaning the optics! Optics can come in contact with contaminants such as dust, water, and skin oils during everyday use. Proper cleaning procedure can maintain the optics’ quality and lifetime. It is important to inspect the optics before cleaning because the order with which the different type of contaminants are removed is important. For example, if an optic is contaminated with both oil and dusts, the dusts should be removed first so that they are not dragged across the delicate optical surface while the oil is being wiped. The cleaning station located near the entrance of the undergraduate photonics lab is equipped with the following supplies:

• Plastic gloves • Canisters of inert dusting gas • Webril wipes (pure cotton) • Edmund lens cleaner (suitable for both glass and plastic optics)

Dusts and loose contaminants Dust and loose contaminants can be blown off using inert dusting gas. Do not blow on the optic surface with your mouth because there will be saliva deposition onto the optics.

1. Hold the can upright (do not shake the can). 2. Start the flow of gas with the nozzle pointed away from the optic to prevent

deposition of gas propellant. 3. Hold the can 10 cm from the optic and use short blasts to clean the optic at a grazing

angle. Liquid and oil contaminants For contaminants that cannot be blown off, Webril wipes and lens cleaning solution should be used. The wipes should always be wet, not dry or dripping. For flat optical surfaces that are elevated above the surrounding surfaces, the drop and drag method can be used:

1. Hold a Webril wipe above the optical surface. 2. Apply a few drops of cleaning solution such that the wipe comes into contact with

the optical surface. 3. Slowly but steadily drag the damp wipe without lifting it off the optical surface. 4. Stop when the wipe is dragged across the entire optical surface.

For curved or mounted optics, the following method sound be used:

1. Fold the Webril wipe a few times. 2. Wet the wipe (use the part of the wipe that was not touched by hand). 3. Apply the wipe to the center of the optic and slowly but continuously rotate the

wipe outward.