Thin Lenses: Locating Images & Magnification Chapter 24: Interference

Hint: Be able to do the homework (both the problems to turn in AND the recommended ones) you’ll do fine on the exam! Monday, February 1, 1999 in class Ch. 22, 23, 24 (Sect. 1-6) You may bring one 3”X5” index card (hand-written on both sides), a pencil or pen, and a scientific calculator with you. Wednesday Instead?

Will not be due until MONDAY, February 1. We have two openings for participation in this study. Those interested in joining the study, please sign the sheet that’s going around. I’ll use random selection to fill the two spots. Commitment is about 15 minutes per week. Reward is 10% class participation bonus.

1) A ray parallel to the principle axis of the lens will be refracted to pass through (or appear to originate from) focal point of the front side of the lens. front back “focus of back surface” “focus of front surface” Converging Lens

1) A ray parallel to the principle axis of the lens will be refracted to pass through (or appear to originate from) focal point of the front side of the lens. [Things look a little different for the diverging lens!] front back “focus of front surface” “focus of back surface” Diverging Lens

2) A ray headed directly toward the center of center of the lens will approximately pass straight through the lens. [This works for the diverging lens as well.] front back focus Converging Lens

3) A ray which passes through (or appears to originate from) the focal point of the back side of the lens will emerge parallel to the principle axis on the back side of the lens. front back “focus of back surface” “focus of front surface”

3) A ray which passes through (or heads directly toward) the focal point of the back side of the lens will emerge parallel to the principle axis on the back side of the lens. [Things look a little different for the diverging lens!] front back “focus of front surface” “focus of back surface” Diverging Lens

Let’s look at the image formed by an object beyond the focal point of a converging lens. front back “focus of back surface” “focus of front surface” IMAGE OBJECT

What is the magnification of a lens? We’ll define it exactly the same way that we’ve done for mirrors and refracting materials... h’ is the image height, h is the object height, q is the image distance, p is the object distance

Whether you’re dealing with mirrors, refracting surfaces, or lenses, p and q are defined to be positive in the direction the light actually travels. Real objects will have p > 0. Real images will have q > 0. Virtual objects will have p < 0. Virtual images will have q < 0.

A double convex thin lens made of glass (n = 1.5) has both radii of curvature of magnitude 20 cm. An object 2 cm high is placed 10 cm from the lens. Find the focal length of the lens, locate the image, and find its size. R 1 = + 20 cm R 2 = - 20 cm R 1 is the radius of curvature of the left surface. It’s behind the lens, so it is (by definition) positive. front back 2cm 10cm R2R2 R1R1

f = 20cm front back 10cm IMAGE

We can now use our formulas to locate the image distance and height more accurately... q = -20cm q < 0, so the image is virtual and on the front side of the lens.

Finally, we compute the size of the image using the formula for magnification... So the image is erect and magnified!

It is extremely important that you work a LOT of the recommended optics problems. These problems aren’t too difficult…IF… you understand the sign conventions! ONLY by working through these for yourself will you learn to correctly apply the sign conventions.

This chapter is a study of the wave properties of light. As we saw with other waves, light waves can interfere with one another, leading to constructive and destructive interference. We’ll examine a couple of ways in which such interference can be produced and demonstrated. Wave Optics

AND

Have you ever been outside, in a large open space, and wandered around as someone spoke over loudspeakers? Depending on where you are on the field, the voice can sound louder or softer.

What’s going on here? Technically, we call it constructive (louder) and destructive (softer) interference. Recall, sound travels in waves (longitudinal pressure waves to be specific). The waves move out in all directions from the two speakers on either side of the stage, arriving at the location on the field at which we happen to be standing.

The sound wave from the left speaker arrives in time t = d(left) / v sound The sound wave from the right speaker arrives in time t = d(right) / v sound d(left) d(right)

If d(right) > d(left), then the sound waves from the left speaker arrive before those from the right speaker. From the left... v sound = 343 m/s From the right... v sound = 343 m/s For a typical audible frequency (3430 Hz), = 10 cm

For this case, the right speaker is exactly 10 cm further away than the left speaker... From the left...From the right... How do I know that? Notice that the blue wave is exactly one wavelength away when the red wave arrives.

So, when the blue wave first arrives, the second crest of the red wave will just be arriving as well. This is a case of constructive interference. The sound will be louder at this spot on the field. From the left...From the right... The crests and troughs arrive from the two speakers simultaneously and in phase!