Online reading assignment: corrective optics, magnifiers

Physics 205B, spring semester 2020
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on corrective optics and magnifiers.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I understood the presentation on myopia. I think it was super cool to see how we are entry-level optometrists after this."

"Refractive power is used by optometrists to measure the degree at which light is converged or diverged denoted by a (+) or (–) sign. It is also the inverse of the focal length."

"The combined total refractive power for two lenses is addition of each refractive power."

"Negative values for the focal length and refractive power mean that corrective lenses should be diverging, to correct for the person's myopia. Corrective lenses with a positive focal length and refractive power will be converging lenses, to correct for hyperopia."

"Magnifiers 'magnify' by increasing the angular size of the object thus making the object appear bigger to the eye. Increasing the distance between the object and the eye provides a smaller angular size and makes the object appear smaller."

"Angular size is the size of an object at a certain distance. The larger the object, the larger the angular size. Magnification isn't really magnifying but rather the lens allows the eye to be able to focus on the object at a distance where it other wise wouldn't have been able to."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Corrective optics. It all seems overwhelming, but simplification will help. Especially refractive power and power addition equations."

"Still figuring out how to work with the thin-lens equations. The steps for correcting myopia and hyperopia were a little confusing."

"I am a little confused on the important difference(s) between linear and angular magnification. I think that I get the basic idea of both but want to make sure I clearly understand how they differ."

"Maybe a little more clarification on the mathematics on angular magnification."

"I did not understand how the eye can perceive the penny to be bigger than the moon. I also did not understand the idea of doing multiple thin lens equations for two lens."

"A review of the equations for angular size and angular magnification would be very helpful. Also I am not really sure about what it exactly means when 'the image is at infinity.'"

"The math seems a little confusing to me right now per usual. But it's late and I'm sleepy."

In general, a converging lens will produce virtual, upright images located __________ the original object.

closer than.	******* [7]
at the same distance as.	** [2]
farther than.	********************** [22]
(Unsure/lost/guessing/help!)	* [1]

In general, a diverging lens will produce virtual, upright images located __________ the original object.

closer than.	************************** [26]
at the same distance as.	[0]
farther than.	***** [5]
(Unsure/lost/guessing/help!)	* [1]

Identify the type of lens used for these optics. (Only correct responses shown.)

Glasses/contacts to correct for myopia: diverging [75%]
Glasses/contacts to correct for hyperopia: converging [78%]
Glasses/contacts to correct for presbyopia: converging [29%]
Magnifying lenses: converging [74%]

State the units of refractive power for lenses, and briefly describe the relationship between refractive power P and focal length f.

"Diopters. Refractive power is 1/f."

"The unit of refractive power for lenses is diopters, which is the inverse of the focal length."

"Units for P are meters^–1."

"I don't understand what this is asking. "

Explain the difference between the two types of magnification, m and M.

"Linear magnification is 'm' and angular magnification is 'M.'"

"m is the ratio of the object's distance or height to the images distance or height at convergence of the light rays h_i/h_o or –d_i/d_o. M is how much the apparent size of something is change by a magnifying lens. The apparent size is an illusion and relative to the viewer."

"m is the ratio of image height to object height while M is a distinct ratio of angular size of some image produced by an optical instrument divided by the reference angular size of an object viewed without an optical instrument."

"I'm not sure what the answer is."

"Again, I am pretty lost."

"Don't remember."

A nominal, relaxed eye is set to focus on objects located at:

+∞.	************ [12]
+25 cm (at your near point).	*********** [11]
+f (at the focal point of the lens).	**** [4]
(Unsure/lost/guessing/help!)	***** [5]

If an object is brought closer to your eye, its angular size will:

increase.	**************************** [28]
decrease.	* [1]
remain unchanged.	[0]
(Unsure/lost/guessing/help!)	*** [3]

When a converging lens is used as a simple magnifier, the object is placed at a distance d_o = __________ in front of (to the left of) the lens.

+∞.	**** [4]
+25 cm (at your near point).	************* [13]
+f (at the focal point of the lens).	********** [10]
(Unsure/lost/guessing/help!)	***** [5]

The ray tracing that best matches when a converging lens is used as a simple magnifier is:

#3.	* [1]
#4.	*************************** [27]
(Unsure/lost/guessing/help!)	**** [4]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can you show a drawing demonstrating the difference between microscope and telescope lens placement and rays? I was confused with presbyopia and how that age-onset disorder works with myopia. (1) In that case someone would be unable to see far--myopia--while simultaneously being unable to see close--presbyopia? Also (2) can someone experience hyperopia and presbyopia or would the condition default to the latter? Finally, while partially off-topic, (3) is there a physics-based description of blindness?" ((1) Yes, someone with myopia (can see near, can't see far) who develops presbyopia (can't see near) would then require bifocals to correct both problems. (2) If you can't see near as a child, you have congenital hyperopia. If you could see near when you were young, but gradually lost that ability as you got older, then you have presbyopia, which is basically age-onset hyperopia, and they are both corrected with a (stronger) converging lens prescription. (3) Not really, I would think that's more of a biology/anatomy/physiology thing.)

"Can we go over problems or see these problems done? When I see these equations being used it makes it easier to understand."

"I have some questions about what a relaxed eye is meant to focus on."

"Please help to understand the angular size and tie all the equations to the ray tracing, this is getting complex."

"I'm not too confident on my answer for how close a simple converging lens used as a magnifier should be."

"I would love more examples of how to guess what kind of ray tracing would apply to real-life situations like a magnifier."

"I think angular magnification is the hardest part of this section, especially when comparing them to ray tracings." (It really is. More on angular magnification next week.)

"Can the human eye control the amount of light that comes in?" (It make less light come in (by making the pupil smaller, or by squinting your eyelids), but it can't make more light coming in than is already there.)

"Do you meditate? Moreover, if you do meditate, do you call it 'total internal reflection?' (Sorry I'm a couple chapters late on this joke.)" (I think my meditation chill is more like something called 'frustrated total internal reflection.' It's when total internal reflection is supposed to happen, but introducing an external object with a new index of refraction that barely touches that surface ruins the total internal reflection, allowing a transmitted ray to go through.)

"How long have you taught physics?" (My first physics class as an instructor was at UC-Davis 26 years ago, when I was still a graduate student.)

Online reading assignment: corrective optics, magnifiers

Physics 205B, spring semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on corrective optics and magnifiers.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Ray tracings are accurate models of how light passes through a lens to create an altered image of the object. The way that the three rays interact with the lens and the focal points determine if the image of the object is: upright or inverted and magnified or diminished."

"The refractive power of contact lens is expressed as the inverse of the focal length. To correct shortsightedness, a diverging lens is prescribed, and for hyperopia, a converging lens is used. The angular magnification measures the angular enlargement or reduction of an object through a lens."

"So basically the two-lens method consists of just getting an image from one lens and then using that image as the next object and thus get another image through the second lens. Which happens with any corrections to your eyesight such as contacts or glasses. I just learned why prescriptions have either the ± sign in front, I can describe how happy I am that I know this now."

"That glasses or contacts over eyes means the light is going through two lenses, the eyes and the contacts. I understood that angular size is not the actual size but the size it relates to the eye from your viewpoint."

"Magnifying glasses do not actually magnify, instead they 'bring' the object closer to the eye. Magnifying glasses allow the eyes to focus on an object when it is closer than 25 cm, the normal point of vision."

"I feel like angular magnification is more intuitive than linear magnification. The angular size of an object is not it's actual size, but it is how large the object appears to be on the retina. This size is given by the angle at which light from the object enters the lens. This is why huge object appear small if they are far away. The far distance creates a small angle."

"The best way to approach optics is to take them one lens at a time. An object goes through one lens to produce an image and then that image is the new object for the second lens. Angular magnification is the way magnifiers work, which allow you to see the object at a greater angular size. This image appears closer and is able to keep the clarity."

"I promise I will read about it this weekend."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I still have trouble applying ray tracings to examples. I think I just have to keep practicing and applying it to things to understand as time goes on."

"I found how optometrists make prescriptions confusing as well as how contacts/glasses actually work when you look at the numbers."

"How the two-lens setup corrects for myopia and hyperopia. I know that the contacts take the object and create an image that the eye is able to see, but I do not understand how the parameters change (focal points and image distance)."

"I don't understand how diopters work, and how the concept of refractive power factors in. I am also a little confused on converging and diverging lenses."

"I am still confused by magnifiers and how they actually work with a relaxed human eye closer or further away from the near focal point of +25 cm. how does this concept compare or relate to the ray tracings?"

"I found everything from the two-lens systems confusing. I don't even know enough to explain what I do or don't know."

"I'm sure you'll go over it in lecture but I could use a bit more explanation on the angular magnification equation."

"Utilizing the equations in problems like homework has also been confusing."

"It would be really helpful if you go over how magnifiers work and what it means when it says focused at infinity."

In general, a converging lens will produce virtual, upright images located __________ the original object.

closer than.	**** [4]
at the same distance as.	** [2]
farther than.	********************** [22]
(Unsure/lost/guessing/help!)	***** [5]

In general, a diverging lens will produce virtual, upright images located __________ the original object.

closer than.	************************** [26]
at the same distance as.	* [1]
farther than.	* [1]
(Unsure/lost/guessing/help!)	***** [5]

Identify the type of lens used for these optics. (Only correct responses shown.)

Glasses/contacts to correct for myopia: diverging [58%]
Glasses/contacts to correct for hyperopia: converging [64%]
Glasses/contacts to correct for presbyopia: converging [33%]
Magnifying lenses: converging [61%]

State the units of refractive power for lenses, and briefly describe the relationship between refractive power P and focal length f.

"m^–1. Refractive power is used to tell the focal length of contact lenses and is the inverse of focal length."

"Diopters. P = 1/f."

"I really don't know...I need help."

Explain the difference between the two types of magnification, m and M.

"Magnification (m) is the ratio of image height to object height and magnification (M) denotes how much larger the angular size of something appears as seen through a magnifier."

"Lower case m is the linear magnification which is the ratio of image length to object length. Capital M magnification is the angular magnification and denotes how much larger the angular size of something appears through a magnifier vs the naked eye."

A nominal, relaxed eye is set to focus on objects located at:

+∞.	****** [6]
+25 cm (at your near point).	************** [14]
+f (at the focal point of the lens).	******* [7]
(Unsure/lost/guessing/help!)	****** [6]

If an object is brought closer to your eye, its angular size will:

increase.	******************* [24]
decrease.	* [1]
remain unchanged.	*** [3]
(Unsure/lost/guessing/help!)	***** [5]

When a converging lens is used as a simple magnifier, the object is placed at a distance d_o = __________ in front of (to the left of) the lens.

+∞.	***** [5]
+25 cm (at your near point).	***** [5]
+f (at the focal point of the lens).	************** [14]
(Unsure/lost/guessing/help!)	********* [9]

The ray tracing that best matches when a converging lens is used as a simple magnifier is:

#3.	******** [8]
#4.	************** [14]
(Unsure/lost/guessing/help!)	*********** [11]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I think more ray tracing in lecture would be helpful. I'm starting to get it, but there's still some doubt."

"This material is harder to understand so hopefully class will clarify my confusion."

"I'm sorry! I have a calculus test and a chemistry test and I need to study really bad :/ "

"Favorite anime?" (Recent favorites? Kill la Kill, Arpeggio of Blue Steel, FLCL (the original series). If you want to get old school, then The Super Dimension Fortress Macross, Space Battleship Yamato, Space Pirate Captain Harlock.) "

Online reading assignment: corrective optics, magnifiers

Physics 205B, spring semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on corrective optics and magnifiers.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Using a two-lens system you can correct for common visual effects. Diopters can be (+) for converging lens and (–) for diverging lens."

"Diverging lenses are used to correct for myopia and that converging lenses are used to correct for hyperopia."

"For two lens systems, the image produced from the first lens is treated as the object for the second lens. I also understand a little bit about how optometrists prescribe corrective glasses to people and the difference between focal length and diopters. Finally, I have a decent understanding of angular magnification works by relating the distance away from the object to the angle at which you are seeing it."

"If you can't see both close and far things, get bifocals."

"I understand what angular size and magnification are. I also get that a 'magnifier' focuses rather than magnifies."

"The two-step model is used in corrective vision as the contact lenses produce a virtual intermediate image at a distance that the eye can focus on. This becomes object 2 for the second lens--the eye--as it turns it into a real image on the retina. If the far point is less than ∞ and/or near point is greater than 0.25 m, then an individual needs corrective optics. Bifocals for have converging lenses for myopia (looking straight) and diverging lenses for hyperopia/presbyopia (looking down for reading)."

"That 'magnifiers' aren't really magnifying, they're playing with angular magnification. By using a magnifying glass you aren't making an object bigger but by placing the object at the focal point of the lens in creates a virtual image that makes it look bigger/closer to you."

"I understood the process of why two lenses are sometimes needed. The first lens produces an intermediate image that the second lens then has to make into the final product. This reminded me of polarized vs non polarized light going through filters--if polarized light passes through two filters, the way it passes through the first directly affects the way it presents through the second filter."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"This is all relatively confusing, as it is a lot of new information to take in. I need in-class reinforcement and repetition as usual :)"

"The contacts/glasses stuff confused me. From the slides I was uncertain how to contact the thin lens equation with the two step model."

"Some parts at the end of the online presentation were a bit confusing. The last few pictures didn't help."

"Angular magnification."

"I found the concept of 'projecting to infinity' confusing. It is hard to comprehend such an abstract idea."

In general, a converging lens will produce virtual, upright images located __________ the original object.

closer than.	****** [6]
at the same distance as.	** [2]
farther than.	******************** [20]
(Unsure/lost/guessing/help!)	* [1]

In general, a diverging lens will produce virtual, upright images located __________ the original object.

closer than.	******************** [20]
at the same distance as.	** [2]
farther than.	****** [6]
(Unsure/lost/guessing/help!)	* [1]

Identify the type of lens used for these optics. (Only correct responses shown.)

Glasses/contacts to correct for myopia: diverging [72%]
Glasses/contacts to correct for hyperopia: converging [72%]
Glasses/contacts to correct for presbyopia: converging [31%]
Magnifying lenses: converging [70%]

State the units of refractive power for lenses, and briefly describe the relationship between refractive power P and focal length f.

"The units of refractive power are P, in units of diopters. This is the inverse of the focal length f, which is measured in meters."

"I have no idea."

Explain the difference between the two types of magnification, m and M.

"Angular magnification M is a value that describes how much larger the angular size of an object appears to be through a magnifier compared to an unaided eye. Meanwhile the linear magnification m is the ratio of image length to object length measured."

"m = linear magnification, while M = angular magnification which tells you how much larger the angular magnification is when looking at an object through a magnifier."

"Unsure."

A nominal, relaxed eye is set to focus on objects located at:

+∞.	*** [3]
+25 cm (at your near point).	****** [6]
+f (at the focal point of the lens).	[15]
(Unsure/lost/guessing/help!)	***** [5]

If an object is brought closer to your eye, its angular size will:

increase.	*********************** [23]
decrease.	***** [5]
remain unchanged.	* [1]
(Unsure/lost/guessing/help!)	[0]

When a converging lens is used as a simple magnifier, the object is placed at a distance d_o = __________ in front of (to the left of) the lens.

+∞.	* [1]
+25 cm (at your near point).	******** [13]
+f (at the focal point of the lens).	******** [8]
(Unsure/lost/guessing/help!)	******* [7]

The ray tracing that best matches when a converging lens is used as a simple magnifier is:

#3.	******** [8]
#4.	************** [14]
(Unsure/lost/guessing/help!)	******* [7]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can we talk about angular magnification?"

"It seems like for presbyopia you would need both types of lenses? But isn't presbyopia similar to hyperopia?" (Yes, presbyopia is basically age-onset hyperopia; even if you can see near now, you will eventually lose that ability as you get older. So if you don't need glasses/contacts now, you'll need reading glasses if you live long enough. However, if you have glasses/contacts to be able to see far (myopia or nearsightedness), you'll need bifocals to also see near when you get old. (If you're still young and have glasses/contacts to be able to see near (hyperopia), you'll just need stronger reading glasses to see near when you get old.)

"I am sorry, I am not there yet. My answers look crazy. Trying to catch up already."

"I feel like everything seems to straightforward in class but then I get to these assignments and I feel so lost :("

"Thank you for all of your hard work in simplifying the text's material on your website (and making it fun)."

"My schedule right now is making things very hard to learn outside of class. The downside to doing the lecture oupside of class class is it can be hard to find the time or space to do this."

"Why does the object's height not mater when we did the ray tracings in lab? Won't that change the distance that the image is from the lens?" (In the thin lens equation (and for ray tracings), the object distance and image distance only depend on each other (and the focal length) of the lens:

(1/d_o) + (1/d_i) + (1/f),

and the object height and image height do not affect the object distance and image distance. However, the object height and image height are related to the object distance and image distance:

(h_i/h_o) = –(d_i/d_o).

Graphically, making the object arbitrarily large or small on a ray tracing just makes the resulting image proportionally large or small as well (stretching or scrunching the vertical dimensions of your ray tracing), but the object distance and image distance (the horizontal dimensions of your ray tracing) are unaffected.)

Online reading assignment: corrective optics, magnifiers

Physics 205B, spring semester 2017
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on corrective optics and magnifiers.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"More about diverging and converging lenses. The diverging lenses will bring an image closer while converging lenses will push an image farther away."

"What I what understood from the blog was the two-step model. I understand how the first image is used as the object for the second image."

"Corrective lenses adjust vision based on an individual's far point and/or near point. The corrective lens adjusts the distance of an object one attempts to see so that it matches their far point and/or near point. The eyes can then focus on the object after it has been 'moved' to the appropriate distance."

"I understand this section pretty well. It is interesting for me to read about glasses (I have worn glasses since I was 3!) I will have to look for my prescription and see what the number is now!"

"This section discussed the different kinds of lenses in contacts and glasses. The contact lens is the first lens, and the eye is the second lens in this two lens system. The focal length of contact lenses are not specified, instead they are rated in terms of refractive power P. In order to figure out the focal point using contacts we have to do calculations."

"The angular size is a measure of how big something seems from your view point. The maximum angular size of an object as seen by an unaided eye is when the object is placed 25 cm away."

"The closer an object, the larger it is perceived and the larger the angle. However, there is a certain extent to which an object can be brought closer in which if it goes too close, it cannot be brought into focus."

"I like how with two-lens systems you can just take it step-by-step. Intermediate image becomes an object, then final image, there's not some strange thing that happens between. It makes sense how a distant d_o corresponds with a small theta, and a near d_o corresponds with a larger θ."

"The more we dive into the subject of refraction of light, the more it all makes sense. Now we are able to use angular magnification to figure out why we see larger images for smaller objects at closer distances than larger objects at further distances."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"What I didn't understand from the reading was the magnifiers. I did not understand the mignifying progress."

"I don't quite understand the idea of being able to focus 'at infinity.' I think it means everything can be focused on. Also, if the image produced by lens 1 is virtual, how can the eyes see it through lens 2?"

"I'm a little confused about myopia and how we correct it."

"What I did not understand from this assignment was the part of the two-step model--I just don't understand the flow of it."

"I think calculating the two-step model for lenses is a little tricky for me. I get a little mixed up on it. It would be very helpful to see an example in class and then it'll probably click. It might be the myopia and different kinds I'm getting mixed up on."

"Kind of weird that magnifying lenses do not magnify, but it makes more sense now."

In general, a converging lens will produce virtual, upright images located __________ the original object.

closer than.	****** [6]
at the same distance as.	* [1]
farther than.	******************* [19]
(Unsure/lost/guessing/help!)	* [1]

In general, a diverging lens will produce virtual, upright images located __________ the original object.

closer than.	****************** [18]
at the same distance as.	[0]
farther than.	******** [8]
(Unsure/lost/guessing/help!)	* [1]

Identify the type of lens used for these optics. (Only correct responses shown.)

Glasses/contacts to correct for myopia: diverging [70%]
Glasses/contacts to correct for hyperopia: converging [78%]
Glasses/contacts to correct for presbyopia: converging [44%]
Magnifying lenses: converging [81%]

State the units of optical power for lenses, and briefly describe the relationship between optical power P and focal length f.

"The units of optical power for lenses is the inverse of meters and there is an inverse relationship between optical power and focal length, as focal length goes down, optical power goes up and vice versa."

"The optical power is measure in diopters, or P, which is the inverse of the focal length or (1/f)."

Explain the difference between the two types of magnification, m and M.

"The small m is linear magnification while the big M is angular magnification."

"Magnification M is the angular size of the image produced by a magnifying glass divided by a reference angular size. Magnification m is a linear measure determined by dividing image height by object height."

"m is virtual and M is real?"

"I am not sure. Will need help clarifying."

If an object is brought closer to your eye, its angular size will:

increase.	********************** [22]
decrease.	** [2]
remain unchanged.	* [1]
(Unsure/lost/guessing/help!)	** [2]

When a converging lens is used as a simple magnifier, the object is placed at a distance d_o = __________ in front of (to the left of) the lens.

+∞.	*** [3]
+25 cm (at your near point).	************ [12]
+f (at the focal point of the lens).	********* [9]
(Unsure/lost/guessing/help!)	*** [3]

The ray tracing that best matches when a converging lens is used as a simple magnifier is:

#3.	******** [8]
#4.	*************** [15]
(Unsure/lost/guessing/help!)	**** [4]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"With polarization, why do we multiply the fraction of first filter to the cos²θ of the second filter when we start with unpolarized light, but not when we start with polarized light and only go through one filter?" (If you have polarized light going through one filter, then the fraction transmitted would be cos²θ. If you have unpolarized light going through a filter, then (1/2) of that light would make it through, and it would then become polarized. If you have unpolarized light going through two filters, then (1/2) of that unpolarized light goes through the first filter making it polarized, and then cos²θ of that polarized light goes through the second filter.)

"A review of ray tracings would be helpful."

"Wearing contacts and glasses myself, this topic is super-interesting to me because I never knew that both were creating a virtual (intermediate) image!"

"It's cool how things become so simple once you understand the formulas for them and the relationships they have with the world."

"I'll be able to remember the difference between the two types of magnification because little m means linear. Little = linear (they both start with L's)."

"I thought I understood this until I began to try to visualize and rationalize what I've learned compared to my experience with a magnifying glass. This stuff takes time to familiarize."

"I am confused why all these math equations implement an inverse? I am confused why the equations cannot work if they are 'un-inversed.'" (Order of operations--inverses (exponent power of –1) go first.)

"I hope there is a lot of explaining going on in lecture... because this stuff is kind of crazy."