Thin lens Definition and 49 Threads

In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses.
The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis.

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  1. Lotto

    Calculate the focal length of a thin convex lens

    My picture is here: The diameter ##D## is also a diameter of the lens. If there was no shade, the image of the moved source would be by using ##\frac{1}{2f}+\frac{1}{L}=\frac 1f## at a distance ##L=2f##. So by using a triangle similarity we get ##\frac{D/2}{L}=\frac{d/2}{L-l}##, so...
  2. L

    Is the image upright for a reflective spherical balloon using ray tracing?

    From ray tracing I would say that the image is upright. Using the equation ##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}## with ##f=-\frac{R}{2}=-2## and ##M=-\frac{q}{p}=\frac{3}{4}## I get ##p=\frac{2}{3}cm\simeq 0.67 cm##. Is this correct? Thanks
  3. P

    Combination of thin lens and concave mirror

    I created the following ray diagram to help me solve the problem: Then I applied the mirror equation 3 separate times. However, the final image distance I got is wrong. I'm wondering if I'm mistaken in taking the last object distance to be negative. However I only have one more try to get this...
  4. Kaelor

    Inserting thick lenses into a thin lens system and deducing values

    Homework Statement:: Finding the distance between the back surface of the first lens and the front surface of the back lens. Homework Equations:: 1/f = 1/s_o + 1/s_i I have two positive thin lenses that are separated by a distance of 5 cm. The focal lengths of the lenses are F_1 = 10 cm and...
  5. J

    Focal length of converging thin lens graphs

    I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p) => M+1= -f/p => -Mp-p=f But since it’s the y intercept, p will equal zero and so the focal length will be 0?
  6. HastiM

    Does the picture change if we turn a thin lens around

    Hello, suppose we are given a thin lens and consider an image of some object formed by that lens. I am wondering what would happen to the image if the thin lens is flipped around (180 degrees)? Of course, if the lens is perfectly symmetric -like for a bi-konvex lens- then the picture should not...
  7. HastiM

    Principal plane of a thin lens

    Hello, in geometric optics people usually say that the refraction of light beams due to a thin lens can be handled by introducing a hypothetical plane (the so called principal plane) at which all the refraction can be considered to happen. But most books only picture the situation for symmetric...
  8. Biker

    Thin lens approximation and Apparent depth

    So we are studying optics in school this semster, Very interseting topic I say but I just have a couple of question I want to ask. In concave and convex mirror, we study spherical ones where F = R/2. I was able to prove this and that it is only an approximation when ## R >> h_o ## or ## h_0##...
  9. Toby_phys

    Compound lens separated by a distance

    Homework Statement Homework Equations We will call ##s## the distance of the object from the first lens, ##s'## the distance of the image from the first lens and ##s''## the distance of the image from the second lens. The Gauss's lens equation: $$\frac{1}{s} +\frac{1}{s'}=\frac{1}{f_1}$$...
  10. JulienB

    When is the image produced by a thin lens sharp?

    Homework Statement Hi everybody! Being given three identical thin lenses with the same focal length, I have to determine ##a## (distance object-screen), ##d_a## (distance lens 1-lens2) and ##d_b## (distance lens 2-lens 3) so that a sharp image of the object appears on the screen regardless of...
  11. Kuzon

    Math in the thin lens equation

    Why isn't 1/f=1/do+1/di just the mathematical equivalent to f=do+di? Can't you raise all terms in the equation to the power of negative 1 to get the latter equation? The maths of reciprocals is confusing me lol.
  12. JohnGaltis

    Double Slit Question with Thin Lens concept

    Homework Statement Consider a double slit experiment with a light source of 540nm. Slit separation is 4mm. A thin glass plate is placed in front of one of the slit,, resulting in each bright fringe moving to the location of the adjacent bright fringe. Find the minimum thickness of the glass...
  13. UchihaClan13

    Refraction Formula For Thin Lens

    I was browsing about my optics books,completing numericals and stuff When I found a a statement called different lens formulas It had 2 formulas One,called the thin lens formula or rather the geometric sign convention formula was called 1/v-1/u=1/f(Symbols have their usual meanings) and another...
  14. G

    How Do You Calculate the System Matrix for a Lens After a Beam Waist?

    Homework Statement A thin lens is placed 2m after the beam waist. The lens has f = 200mm. Find the appropriate system matrix. This is a past exam question I want to check I got right. Homework Equations For some straight section [[1 , d],[0 , 1]] and for a thin lens [[1 , 0],[-1/f , 1]]...
  15. D

    Radiative Transfer Equation: Point Source and a Thin Lens

    Homework Statement Write the Radiative Transfer Equation for an isotropic incoherent point source a distance p away from a thin lens. Assume that scattering in air can be ignored but absorption cannot be ignored. Homework Equations 1. Radiative Transfer Equation (RTE): \frac{dw}{dt} = \left[...
  16. S

    Where to place a thin lens to couple a ray into a fiber

    Homework Statement i need to couple a ray (point source 15 deg) into a fiber with a small core diameter, the fiber located 8cm from the source. the focal distance of the lens is 1.5cm i need to choose 2 possible locations Homework EquationsThe Attempt at a Solution first suggestion: i placed...
  17. brianeyes88677

    Understanding the Focal Plan of Parallel Light Through a Thin Lens

    Why does parallel light focus on the focal plan when enters a thin lens at an angle θ? How to proof that mathematically?
  18. M

    Focal length from thin lens to object distance

    Hello, I've come across an problem that requires the lens to be at least about 350 mm away from the object. Object to be examined is 80 mm tall and imaging plane is either 11 mm or 25 mm tall. I've tried to calculate required focal length, but have not succeeded. Distance from lens to imaging...
  19. C

    Thin lens equation and image formation

    Homework Statement An object 4.29 cm high is projected onto a screen using a converging lens with a focal length of 32 cm. The image on the screen is 51.7 cm. Where are the lens and the object located relative to the screen? ho=4.29 cm hi=51.7 cm ƒ=32 cm Homework Equations 1...
  20. G

    What is the solution for object distance in a diverging lens?

    Homework Statement Now consider a diverging lens with focal length f=−15cm, producing an upright image that is 5/9 as tall as the object. What is the object distance? You will need to use the magnification equation to find a relationship between s and s′s′. Then substitute into the thin lens...
  21. B

    Thin Lens Equation: Nearsighted

    Homework Statement For those fortunate souls who do not need glasses, the lens of the eye adjusts its focal length in order to form a proper image on the retina. This typically means that very distant objects as well as objects as close as 25 cm can be seen clearly. Many of us need...
  22. I

    Finding fmax in Thin Lens Refraction Problem

    Homework Statement Hi all. This is a problem from one of the problem sheets from earlier in the term. I'm just revising for my exam tomorrow and can't solve this one. Here it is: Consider a light source placed at a fixed distance L from a screen, such that a lens of focal length f can be...
  23. B

    Understanding Thin Lens Equations: Solving for Image Distances and Focal Length

    Homework Statement I am given 5 distances to place the object relative to the lens. I then need to calculate each of the images distances for all 5 and record them. Once I have that done, I am to conduct a graph of 1/q vs 1/p. I then need to answer these questions: 1- Is the slope of your...
  24. N

    Thin Lens Formula: Deriving 1/f = 1/S_O + 1/S_I

    Hi The thin lens equation we know is given by \frac{1}{S_O} + \frac{1}{S_I} = (n-1)(\frac{1}{R_1}-\frac{1}{R_2}) assuming light is incident from air. The "usual" way to derive the thin lens formula (aka the Gaussian Lens Formula) is to say that when looking at the system when either the...
  25. Q

    Derivation of the thin lens equation?

    'm currently reading chapter 27 of the Feynman lectures, where he derives the thin lens equation for a single refracting surface. He arrives at the equation h^2/2s + nh^2/s' = (n-1)h^2/2r Where s is the object distance, s' is the image distance, n is the index of refraction of the second...
  26. L

    Are the Radii R1 and R2 of a Lens Always the Same?

    Homework Statement A lens is a transparent refracting medium bounded by two spherical surfaces.R1 and R2 are radii of two surfaces. Homework Equations Will the Radii R1 and R2 will be same or different ? The Attempt at a Solution I hope that they are same, otherwise there won't...
  27. A

    How Is Magnification Calculated with Two Thin Lenses?

    Homework Statement A light source placed in the focus of a (thin) lens with a focal length of 50mm. A second (thin) lens (with focal length = 400mm) was placed 600mm after the focal point of the first one, an image of the light source was captured at the seonds lens focal point. How...
  28. fluidistic

    Plano-concave thin lens, checking my result

    Homework Statement Determine the focal length of a plano-concave lens (n=1.5) which has a radius of curvature of 10 cm. What is its power in diopters? Homework Equations None given. The Attempt at a Solution 1/f=(n-1)(1/R_1-1/R_2)=(1/2)(-0.1)=-1/20. Thus f=5 cm and P=-20 m^(-1)...
  29. fluidistic

    Prove 4f is the Min. Distance Between Conjugate Points for Thin Lens

    Homework Statement Show that the minimum distance between 2 conjugate points (real object and image) for a positive thin lens is 4f.Homework Equations \frac{1}{f}=\frac{1}{S_o}+\frac{1}{S_i}.The Attempt at a Solution I assumed the lens to be biconvex (though I know that I can't. There are so...
  30. L

    Understanding Thin Lens Formula: Image Location & Projection

    Hi, in questions involving lenses, when using the "thin lens formulae" if my di is negative doesn't that mean the image is on the other side of the lens? in this example however it doesn't seem this holds true.. A doctor examines a patient's skin lesion with a 15 cm focal length...
  31. G

    Thin Lens & Images: Real, Inverted & Smaller Objects

    Homework Statement Under what conditions will a thin converging lens form: a) a real image, b) an inverted image, and c) an image smaller than the object? Homework Equations none The Attempt at a Solution I have concluded that: a) the object needs to be outside the focal...
  32. N

    Optics: Ray matrix for a thin lens

    Hi guys I wonder if you can explain this to me. In http://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis#Table_of_ray_transfer_matrices it says under "Thin lens" that the ray matrix is given by \left( {\begin{array}{*{20}c} {r_{final} } \\ {r_{final}^' } \\ \end{array}} \right) =...
  33. G

    How Does Refraction Affect Image Location in a Thin Lens Observation?

    Homework Statement A small fish, four feet below the surface of Lake Lansing is viewed through a simple thin converging lens with focal length 30 feet. If the lens is 2 feet above the water surface, where is the image of the fish seen by the observer? Assume the fish lies on the optical axis...
  34. O

    Optical Instruments I - Thin Lens

    Homework Statement part1: In the Figure below a lens of focal length 8 cm is placed between a plane mirror and a pin hole. The other side of the pin hole is illuminated by a light source (not shown), so that the light passes through the hole and is then collected by the lens. If the pin hole...
  35. C

    Optics: Thin Lens and Image Formation

    Homework Statement A student is working in an optics lab and has a light bulb which is 100 cm from a screen. She needs to make a real image a real image of the bulb on the screen and she has a converging lens with a focal length of +15 cm. Find two places she can put the lens and give object...
  36. F

    Thin lens equation with multiple lenses

    Homework Statement Heres the problem exactly as written: A system of lenses is composed of three lenses. Calculate the maximum magnification these three lenses will achieve if the lenses are located 35.0 cm apart. The lenses have focal lengths of 15.0, 20.0, and 25.0 cm.Homework Equations 1/p...
  37. M

    Geometric optics - why inverted image from thin lens

    Three questions: 1) Anyone have a pedagogic answer to why the image formed by a thin lens is inverted (i.e. upside-down)? I realize that to get a focused image, the lens has to converge the rays one way or another, so then, eventually, the rays have to cross the optic axis, which in turn...
  38. J

    Finding the Distance for Enlargement with a Thin Lens

    If you want to produce an image of a bulb that is enlarged by a factor of 2, how far from the wall should the lens be placed. Focal length is 40cm. I know you use 1/d_o + 1/d_i =1/f and m= -d_i/d_o but how do you find d_o? -2/d_o +1/d_o =1/f ? but it comes out to 40cm and not 60cm...
  39. L

    Understanding the Thin Lens Equation: How to Graph and Interpret Results

    I need to learn how to graph do=1/(f -1/di) like i have my measurements and when i plug in my di i get a do so what do i do with my old do?
  40. L

    How Do Similar Triangles Derive the Thin Lens Equation?

    kk so i found out the steps involved deriving the thin lens equation, but what i don't get is when you have 2 similar triangles say triangle abd,edf are congruent how does the 2 triangles make it so its di/f-1. so what I am basically asking is can someone thourougly explain to me what's going on...
  41. L

    Deriving the Thin Lens Formula: How Does Equation 1 Relate to the Triangles?

    Hi I need help on figuring where and how 1/f = 1/do + 1/di My teacher told me it relates to the ray diagram but i have no clue where to start to find where this formula has come from. Any help would be much appreciated.
  42. N

    Thin lens equation for diverging lenses.

    Hi, I was reading a section which explains about the "thin lens equation for diverging lenses" and it included an example; Formula: 1/f = 1/di + 1/do where f is the focal distance, di is the distance of the image from the center and, do is the distance of the object from the center. Example: f...
  43. J

    Thin Lens Equation - Hypothesis

    Homework Statement Hi, I am writing a lab report, and I have no idea how to come up with a fitting hypothesis for this lab Purpose: To determine the relationship among the focal length, the image distance, and the object distance of a converging lens.
  44. M

    What Does t Represent in Interference Without a Lens?

    Homework Statement A source S of monochromatic light and a detector D are both located in air a distance of h above a horizontal plane sheet of glass, and are separated by a horizontal distance of x. Waves reaching D directly from S interfere with waves that reflect off the glass. The...
  45. B

    Thin Lens Equation - How to Solve for the Position of a Converging Lens

    Homework Statement 3. A converging lens has a focal length of 10 cm. A screen is placed 30 cm from an object. Where should the lens be placed, in relation to the object, to produce a focused image?Homework Equations 1/do + 1/di = 1fThe Attempt at a Solution Do can not be greater than 2F...
  46. S

    Solve Thin Lens Equation: Diverging Lens, Virtual Image

    I am stuck on this problem because it been like 6 yrs since i took geometry and its due by 9 am. please help! Derive the thin lens equation: 1/object distance + 1/ image distance = 1/focal length for a divergent lens, using a diagram of a divergent lens (hint: use similar triangles)...
  47. A

    Solving Thin Lens Formula Problems

    I have to complete a chart using the thin lens forumla. Can someone please help me out? I know that the formula is 1/f= 1/do= 1/di, but I don't know how to use it. Thanks.
  48. N

    Converging Lens Problem: Finding Distance from Slide for Real and Virtual Images

    A transparent photographic slide is placed in front of a converging lens with a focal length of 2.24 cm. The lens forms an image of the slide 11.4 cm from the slide. (a) How far is the lens from the slide if the image is real? (b) How far is the lens from the slide if the image is virtual...
  49. K

    Thin Lens Exp: Prove Linear Graph, Determine Slope and Intercept

    Hi, I'm first year Engineering in the Phys1130 course at my college and I've ended up hitting a large brick wall with the pre-lab. The pre-lab section of the experiment goes: "The thin lens equation is: (1/do) + (1/di) = (1/f) di = distance from lens to image do = distance from...
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