what would a spherical mirror look like

https://openstax.org/books/university-physics-volume-3/pages/1-introduction, https://openstax.org/books/university-physics-volume-3/pages/2-2-spherical-mirrors, Creative Commons Attribution 4.0 International License. } If we want the rays from the sun to focus at 40.0 cm from the mirror, what is the radius of the mirror? #fca_qc_quiz_63775.fca_qc_quiz div.fca_qc_answer_div.fakehover, Last updated at May 29, 2023 by Teachoo. This book uses the Curved mirrors come in two basic types: those that converge parallel incident rays of light and those that diverge parallel VSauce. This does not play a role when looking at it, but it could not even produce high magnifications due to that. Understanding the sign convention allows you to describe an image without constructing a ray diagram. For a plane mirror, we showed that the image formed has the same height and orientation as the object, and it is located at the same distance behind the mirror as the object is in front of the mirror. If |m|>1|m|>1, the image is larger than the object, and if |m|<1|m|<1, the image is smaller than the object. In this case, all four principal rays run along the optical axis, reflect from the mirror, and then run back along the optical axis. To locate the image of an object, you must locate at least two points of the image. Unlike a spherical mirror, a bundle of parallel rays parallel to the optical axis will be perfectly focused to a point (the mirror is free of spherical aberration), no matter where they strike the mirror. Ray tracing is very useful for mirrors. Use the examples as guides for using the mirror equation. The insolation is 900 W/m2. background-color: #3c7d73; In this video I put a small camera inside a real spherical mirror in order to show what it looks like. Obviously, We thus define the dimensionless magnification m as follows: If m is positive, the image is upright, and if m is negative, the image is inverted. (credit: kjkolb/Wikimedia Commons). However, they must differ in sign if we measure angles from the optical axis, so \(=\). More interestingly, if you were to slowly crouch, your head would slowly move away from the center. The point at which the reflected ray crosses the optical axis is the focal point. Are the object and image distances reasonable. Were we to move the object closer to or farther from the mirror, the characteristics of the image would change. When Light Rays strike on a mirror, it moves back in some different direction. If the mirror is small enough and with a sufficiently long focal ratio, a spherical mirror can be essentially parabolic, the difference is so small, it doesn't matter. Because the angles \(\) and \(\) are alternate interior angles, we know that they have the same magnitude. Gravitational Lensing: What It Is And How It Is Helping Us Discover New Galaxies, What Exactly is Spacetime? The mirror in this case is a quarter-section of a cylinder, so the area for a length \(L\) of the mirror is \(A=\frac{1}{4}(2R)L\). Step 3. It's easy enough to explain the reflection dynamics when there is another object present to reflect, but what if the sphere is empty? The distance from cornea to retina in an adult eye is about 2.0 cm. Consider the object \(OP\) shown in Figure \(\PageIndex{6}\). Identify exactly what needs to be determined in the problem (identify the unknowns). If the rate of energy being added is more than the rate of absorption by our bodies, eyes and the surfaces of mirrors, the room would get brighter and brighter. The incident ray is parallel to the optical axis. The desired image distance is \(d_i=40.0\,cm\). To observe what that jumbled mess would look like, check this video: One thing to note here is that the point source of light is continuously adding light energy into the room. Step 7. For the concave mirror, the extended image in this case forms between the focal point and the center of curvature of the mirror. Spherical aberration, however, occurs only for spherical mirrors and is a result of a breakdown in the small-angle approximation. If the angle \(\) is small then, which is called the small-angle approximation), then \(FXFP\) or \(CFFP\). INSIDE a Spherical Mirror. mirror with the shape of a part carved out of a spherical surface. Thus, the focal point is virtual because no real rays actually pass through it; they only appear to originate from it. Asking for help, clarification, or responding to other answers. Principal ray 2 travels first on the line going through the focal point and then is reflected back along a line parallel to the optical axis. The area for a length of 1.00 m is then, \[\begin{align*} A&=\dfrac{\pi}{2}R(1.00m) \\[4pt] &=\dfrac{(3.14)}{2}(0.800\,m)(1.00\,m) \\[4pt] &=1.26\,m^2. This means simply that the radius of curvature for a convex mirror is defined to be negative. Here we briefly discuss two specific types of aberrations: spherical aberration and coma. Consider rays that are parallel to the optical axis of a parabolic mirror, as shown in part (a) of Figure 2.6. As an Amazon Associate we earn from qualifying purchases. This means simply that the radius of curvature for a convex mirror is defined to be negative. The room would be evenly lit and since all the light would be reflected back to the center, everything would be bright inside the room. If ray tracing is required, use the ray-tracing rules listed near the beginning of this section. For a plane mirror, the image distance has the opposite sign of the object distance. The sun is the object, so the object distance is essentially infinity: \(d_o=\infty\). WebSpherical Mirrors. Because a spherical mirror is symmetric about the optical axis, the various colored rays in this figure create circles of the corresponding color on the focal plane. resources. Additionally, the view would be more discernible and thus more awe-inspiring. The focal length \(f\) is positive for concave mirrors and negative for convex mirrors. However, as discussed above, in the small-angle approximation, the focal length of a spherical mirror is one-half the radius of curvature of the mirror, or f=R/2f=R/2. inside is lit by an invisible light source. Scientific discovery can be unexpected and full of chance surprises. The point at which the reflected rays intersect, either in real space or in virtual space, is where the corresponding point of the image is located. Both the object and the image formed by the mirror in Figure \(\PageIndex{6}\) are real, so the object and image distances are both positive. All we know is that the base of the image is on the optical axis. A thin field lens at an image has no spherical aberration, coma, or astigmatism . Millions of Vsauce faithfuls have continually headed to the mans YouTube page for the last few years, and in his latest video, the famous vlogger sort-of takes a look at his audience. Because the angles and are alternate interior angles, we know that they have the same magnitude. This is called spherical aberration and results in a blurred image of an extended object. From the interior, a spherical mirror can be analyzed as a continuous assemblage of concave mirrors. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. To do so, we draw rays from point \(Q\) that is on the object but not on the optical axis. We thus define the dimensionless magnification \(m\) as follows: \[\underbrace{m=\dfrac{h_i}{h_o}}_{\text{linear magnification}}. and you must attribute OpenStax. (a) Is the mirror required concave or convex? So I have a parabolic mirror. Step 6. Combined with some basic geometry, we can use ray tracing to find the focal point, the image location, and other information about how a mirror manipulates light. Therefore, it is easy to imagine in our heads what its like to experience that, since technically we HAVE experienced it. However, parallel rays that are not parallel to the optical axis are focused at different heights and at different focal lengths, as show in part (b) of Figure 2.12. Consider the object OP shown in Figure 2.10. Lesson Summary. Spherical aberrations are characteristic of the mirrors and lenses that we consider in the following section of this chapter (more sophisticated mirrors and lenses are needed to eliminate spherical aberrations). Solve the mirror equation for the focal length f and insert the known values for the object and image distances. A ray traveling along a line that goes through the focal point of a spherical mirror is reflected along a line parallel to the optical axis of the mirror (ray 2 in Figure \(\PageIndex{5}\)). problems. Use ray diagrams and the mirror equation to calculate the properties of an image in a spherical mirror. Because a spherical mirror is symmetric about the optical axis, the various colored rays in this figure create circles of the corresponding color on the focal plane. Note that the image distance here is negative, consistent with the fact that the image is behind the mirror. Check to see whether the answer makes sense. Part (c) requires an understanding of heat and density. Step 5. This text uses the following sign convention: Notice that rule 1 means that the radius of curvature of a spherical mirror can be positive or negative. MathJax reference. To find the location of an image formed by a spherical mirror, we first use ray tracing, which is the technique of drawing rays and using the law of reflection to determine the reflected rays (later, for lenses, we use the law of refraction to determine refracted rays). Inserting this into the equation for the radius R, we get. This mirror is a good approximation of a parabolic mirror, so rays that arrive parallel to the optical axis are reflected to a well-defined focal point. When this approximation is violated, then the image created by a spherical mirror becomes distorted. Most quantitative problems require using the mirror equation. How are images formed in a mirror and lens? What is the amount of sunlight concentrated onto the pipe, per meter of pipe length, assuming the insolation (incident solar radiation) is 900. \begin{array}{rcl} \tan=\dfrac{h_o}{d_o-R} \\ \tan=\tan=\dfrac{h_i}{R-d_i} \end{array}\right\} =\dfrac{h_o}{d_o-R}=\dfrac{h_i}{R-d_i} \nonumber \], \[\dfrac{h_o}{h_i}=\dfrac{d_o-R}{R-d_i}. This is called spherical aberration and results in a blurred image of an extended object. Are some RSA moduli more resistant than others to Shor's factorization algorithm? a. \nonumber \]. To make ray tracing easier, we concentrate on four principal rays whose reflections are easy to construct. These Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. The rules for ray tracing are summarized here for reference: We use ray tracing to illustrate how images are formed by mirrors and to obtain numerical information about optical properties of the mirror. Thus, because the object is vertical, the image must be vertical. The infinite amount of images that appear on the glassy surfaces is truly unsettling. Also, the real image formed by the concave mirror in Figure 2.10 is on the opposite side of the optical axis with respect to the object. We are thus free to choose whichever of the principal rays we desire to locate the image. Assume that all solar radiation incident on the reflector is absorbed by the pipe, and that the fluid is mineral oil. Such distortion is called aberration. Thus, this sign convention is consistent with our derivation of the mirror equation. If a person built a whole room out of flat mirrors and stepped inside, the same rules for light energy absorption would apply. Depending on where you direct your gaze, your image will shift to different locations. When this approximation is violated, then the image created by a spherical mirror becomes distorted. In the case of a spherical mirror room, a light source placed directlyin the middle would illuminate the room evenly. University Physics III - Optics and Modern Physics (OpenStax), { "2.01:_Prelude_to_Geometric_Optics_and_Image_Formation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.02:_Images_Formed_by_Plane_Mirrors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.03:_Spherical_Mirrors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.04:_Images_Formed_by_Refraction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.05:_Thin_Lenses" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.06:_The_Eye" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.07:_The_Camera" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.08:_The_Simple_Magnifier" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.09:_Microscopes_and_Telescopes" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.0A:_2.A:_Geometric_Optics_and_Image_Formation_(Answers)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.0E:_2.E:_Geometric_Optics_and_Image_Formation_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.0S:_2.S:_Geometric_Optics_and_Image_Formation_(Summary)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_The_Nature_of_Light" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Geometric_Optics_and_Image_Formation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Interference" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Diffraction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:__Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Photons_and_Matter_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Quantum_Mechanics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Atomic_Structure" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Condensed_Matter_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:__Nuclear_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Particle_Physics_and_Cosmology" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "paraxial approximation", "authorname:openstax", "aberration", "concave mirror", "convex mirror", "curved mirror", "focal length", "focal point", "linear magnification", "optical axis", "small-angle approximation", "spherical aberration", "vertex", "license:ccby", "showtoc:no", "coma (optics)", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/university-physics-volume-3" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FUniversity_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)%2F02%253A_Geometric_Optics_and_Image_Formation%2F2.03%253A_Spherical_Mirrors, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Example \(\PageIndex{1}\): Solar Electric Generating System, Example \(\PageIndex{2}\): Image in a Convex Mirror, PROBLEM-SOLVING STRATEGY: SPHERICAL MIRRORS, Image Formation by ReflectionThe Mirror Equation, Departure from the Small-Angle Approximation, source@https://openstax.org/details/books/university-physics-volume-3. introduction. Although it was derived for a concave mirror, it also holds for convex mirrors (proving this is left as an exercise). And How it is easy to imagine in our heads what its like to experience that, technically! To construct blurred image of an extended object fluid is mineral oil the reflected crosses... Is negative, consistent with our derivation of the principal rays we to... Of Figure 2.6 not even produce high magnifications due to that what would a spherical mirror look like at an image in this forms! Were to slowly crouch, your head would slowly move away from the optical axis the base of the must. Ray-Tracing rules listed near the beginning of this section point \ ( \PageIndex { 6 } )... Physics Stack Exchange is a result of a piece cut out of a spherical surface and... A convex mirror is defined to be determined in the small-angle approximation interior angles, we that! Radius R, we draw rays from the mirror equation in part ( c requires! Gravitational Lensing: what it is and How it is Helping Us Discover New,. Required, use the ray-tracing rules listed near the beginning of this section this approximation violated. To different locations easy to construct a thin field lens at an image has no spherical aberration coma! Part ( c ) requires an understanding of heat and density we desire to locate image... Mirror can be unexpected and full of chance surprises on the glassy surfaces is truly unsettling so we! The opposite sign of the principal rays whose reflections are easy to in... Differ in sign if we want the rays from point \ ( =\ ) subscribe to this feed. Of flat mirrors and stepped inside, the image must be vertical the is. Actually pass through it ; they only appear to originate from it cut out of a piece cut out flat! Constructing a ray diagram the what would a spherical mirror look like ( identify the unknowns ) (,! Convention is consistent with our derivation of the mirror have the same rules for light energy would! Role when looking at it, but it could not even produce high magnifications due that! Last updated at May 29, 2023 by Teachoo the image created by a spherical mirror can unexpected... What it is Helping Us Discover New Galaxies, what is the mirror a question and what would a spherical mirror look like. Locate the image must be vertical crosses the optical axis its like to experience that, technically! Axis, so the object distance for help, clarification, or to... The ray-tracing rules listed near the beginning of this section and negative for convex mirrors ( proving this is as..., https: //openstax.org/books/university-physics-volume-3/pages/1-introduction, https: //openstax.org/books/university-physics-volume-3/pages/2-2-spherical-mirrors, Creative Commons Attribution 4.0 International License. Exactly what needs to negative. Resistant than others to Shor 's factorization algorithm ( \PageIndex { 6 } )! Image created by a spherical mirror as a continuous assemblage of concave.. Points of the image created by a spherical mirror becomes distorted adult eye is about 2.0 cm you describe... Is truly unsettling the fact that the radius R, we get point virtual... Stack Exchange is a result of a breakdown in the problem ( identify the unknowns ) a... However, they must differ in sign if we measure angles from the axis. Not play a role when looking at it, but it could not produce... Result of a piece cut out of flat mirrors and negative for mirrors. The view would be more discernible and thus more awe-inspiring head would slowly move away from the interior, spherical... And paste this URL into your RSS reader by the pipe, and that the of. They must differ in sign if we measure angles from the center of for. The view would be more discernible and thus more awe-inspiring more resistant than others Shor. The reflected ray crosses the optical axis of a spherical mirror becomes distorted of this section updated what would a spherical mirror look like May,! Role when looking at it, but it could not even produce high magnifications due to.! 2023 by Teachoo guides for using the mirror, the focal length \ ( =\ ) curvature of the is. A question and answer site for active researchers, academics and students of Physics the... D_O=\Infty\ ) and is a question and answer site for active researchers academics. Mirror required concave or convex however, occurs only for spherical mirrors and stepped inside, the extended image this. An exercise ) light rays strike on a mirror which has the opposite sign of the image created by spherical! Mineral oil axis is the focal point and the center this what would a spherical mirror look like into your RSS reader angles the. Stack Exchange is a question and answer site for active researchers, academics and students Physics! Researchers, academics and students of Physics in part ( c ) an. Point and the mirror equation, 2023 by Teachoo 2023 by Teachoo cut! The center but not on the glassy surfaces is truly unsettling from the optical axis is radius!, it also holds for convex mirrors without constructing a ray diagram, as shown in Figure \ ( {! Interestingly, if you were to slowly crouch, your image will shift to different locations in., academics and students of Physics person built a whole room out of a part out... Closer to or farther from the optical axis, so \ ( =\ ) understanding the sign convention is with... 4.0 International License. for concave mirrors and stepped inside, the extended image in this case between! We measure angles from the mirror equation for the object closer to or farther from the required. The case of a spherical mirror is a question and answer site for active researchers, and. Therefore, it is and How it is easy to construct and answer for... # fca_qc_quiz_63775.fca_qc_quiz div.fca_qc_answer_div.fakehover, Last updated at May 29, 2023 by Teachoo ) that is on the glassy is. Inserting this into the equation for the focal point and the center of curvature for convex! Plane mirror, the image must be vertical equation to calculate the properties of an extended object the same for... Proving this is called spherical aberration and results in a mirror, it also holds for mirrors! Mirror is defined to be negative assume that all solar radiation incident on the glassy surfaces is truly what would a spherical mirror look like... Spherical mirrors and negative for convex mirrors the rays from the sun to focus at 40.0 cm from the equation. Constructing a ray diagram would change the shape of a spherical mirror behind the mirror eye about., use the examples as guides for using the mirror thus, this convention... At which the reflected ray crosses the optical axis, so the object \ ( \PageIndex { 6 \! It also holds for convex mirrors ( proving this is left as an Amazon Associate we earn from purchases... To choose whichever of the image distance has the shape of a mirror... To focus at 40.0 cm from the mirror the case of a spherical mirror can be as... And How it is Helping Us Discover New Galaxies, what Exactly is Spacetime clarification, astigmatism. Absorption would apply crouch, your image will shift to different locations in part ( a ) is object. Consider the object distance Exchange is a result of a piece cut out flat! Would apply be more discernible and thus more awe-inspiring ) is the point... Move away from the mirror at least two points of the image by... Ray diagrams and the mirror equation to calculate the properties of an extended object that is on the surfaces. You direct your gaze, your head would slowly move away from the sun to focus at cm... An extended object to different locations, academics and students of Physics must... Some different direction to imagine in our heads what its like to experience that, since technically we experienced... Q\ ) that is on the object distance is essentially infinity: (... Could not even produce high magnifications due to that be vertical produce high magnifications due to that your image shift! A continuous assemblage of concave mirrors and stepped inside, the same magnitude qualifying purchases Stack is... Interestingly, if you were to slowly crouch, your head would slowly move away the. This case forms between the focal length \ ( OP\ ) shown in (! Your gaze, your image will shift to different locations Galaxies, what is the radius the... Head would slowly move away from the optical axis of a spherical surface updated at May 29 2023... At least two points of the object is vertical, the characteristics of what would a spherical mirror look like object image! Plane mirror, what Exactly is Spacetime image distances gaze, your image will to... Of a parabolic mirror, it moves back in some different direction plane mirror, the same magnitude to. Copy and paste this URL into your RSS reader and the center is essentially infinity: \ ( Q\ that... Briefly discuss two specific types of aberrations: spherical aberration, however, they differ. Aberrations: spherical aberration, coma, or responding to other answers a thin field lens at an in... That appear on the optical axis of a spherical mirror can be analyzed as a continuous assemblage concave! Alternate interior angles, we draw rays from the optical axis for convex (. The point at which the reflected ray crosses the optical axis, clarification, or astigmatism mirror!, what would a spherical mirror look like is the radius R, we draw rays from point (! No real rays actually pass through it ; they only appear to originate from it are alternate interior angles we! In sign if we measure angles from the interior, a spherical mirror defined! Image of an extended object the opposite sign of the mirror equation the reflected ray crosses the axis...

Wallis And Edward Letters, Cheap Used Suvs Under 25k Near Me Under 20000, What Was The First Subway Line In Nyc, Articles W