What is Focal length: Definition and 235 Discussions

The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power.
In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view; conversely, shorter focal length or higher optical power is associated with lower magnification and a wider angle of view. On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length (higher optical power) leads to higher magnification because the subject can be brought closer to the center of projection.

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  1. Lotto

    Calculate a radius of a circle on a screen

    The picture is here. The radius should be ##R=2.94\,\mathrm {cm}##. In the original solution, it is solved by using a critical angle ϵm. The b is the maximum distance at which a beam can refract. I understand this solution and an image of it is here: But I wanted to calculate it by knowing...
  2. 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...
  3. ilovemycat

    Graphically determining the focal length of a converging lens

    So I have plotted all the given data points on a graph, putting 1/di on the y- axis and 1/do on the x-axis. I have to now find focal length from the graph? I'm not sure how, I'm thinking I have to rearrange the equation 1/f = 1/do + 1/di into y = mx + b form then go from there, but I'm totally...
  4. Lotto

    What is a focal length of a thin convex lens?

    I think that there might be several solutions. I drawed one possible situation: I think that this is just geometry, but I don't know how to solve it simply. I had an idea that if the beam was going through the black axis, then it would be easy to calculate, and that would be aslo solution for...
  5. ab200

    Destroying a Building Using a Lens

    Putting the questionable nature of my professor's problem-writing aside, I found this question pretty confusing. I assumed that 60 m was the focal length, and that R1 was infinity since it is a flat surface. This gives me: 1/60 = (1.5 - 1)[(1/∞) - (1/R2)] This gave me R2 = 30 m, but that isn't...
  6. D

    The patient is myopic

    Its near point is 13.0 cm from the eyes and its far point is 50.0 cm. a) What type of contact lenses should be prescribed to correct his nearsightedness. Determine their focal length b) Determine the near point of the patient when using lenses for the correction of myopia.
  7. F

    I How to calculate focal length?

    Hello, I am new to this forum and know very little about it. But perhaps somebody can help me. I have an Epson 2040 projector. The beam it projects fits into the screen at a distance of about 4.5 meters. But logistically I need to put it at 8 meters from the screen, so the projected images are...
  8. thementalist123

    What is the Focal Length of a Lens for a Perfectly Fitting Image on a Sensor?

    My attempt: m=-v/u=-f/(-f-u) -1/0.5= -f/-f-0.10 -> -f-0.10=0.5f -> f=0.20 m
  9. Aymangh994

    I Total focal length and magnification

    I would like to realize an image of the cantilever. The dimensions are (450x50) microns. I would like to use a self-constructed telephoto lens. This consists of two lenses. The image magnification can be 4 to 8. The magnification of the image is nothing more than the ratio between the two focal...
  10. Aymangh994

    I Using simple lenses to image AFM Probes

    Hello, Using a CCD camera and simple lenses, the probe of the cantilever and its surroundings are to be imaged. Since the cantilever is 50 um wide and some of the surroundings are to be imaged, the optimal image magnification is from 4 to 8. I therefore used a convex lens with a focal length of...
  11. Melbourne Guy

    Focal length of LCD screen as a car's rear view mirror

    I noticed on the commute home today a car with a LCD rear view mirror and I wondered whether, if I were driving it, I'd be able to focus on it the same as I focus on my car's glass review view mirror? I need glasses to read, and that includes a computer, so figured a LCD screen that close, even...
  12. bluesteels

    How do you know if the focal length is positive or negative?

    In this problem, it doesn't tell you where is the focal length. So how do you know if it is in front or behind the object?
  13. VVS2000

    I Finding focal length of the lens using "u-v" method

    I was just checking out this experiment for finding focal length of a lens that I did few years back. the method used was called as the u-v method(https://www.concepts-of-physics.com/pdf/uv-method.pdf), and here in this method, object distance u and image distance v is measured from the sharp...
  14. Istiak

    Find focal length of electron for a parabolic motion

    Here I was going to use ##\int \vec F \cdot d\vec l = \frac{1}{2}mu^2## What I got that is ##l=\frac{mu^2}{2eE}##. Here the question is what is ##l## (I took ##x## while doing the work but here I used ##l## instead of ##x##)? I was assuming that it's ##x## since I am calculating work in the...
  15. Horizont22

    I Shorten the lens distance while having same focal length?

    Hello Everybody, I'm David from Spain, and happy to be here. We have a LED that needs a FL50mm collimator which is focused to infinite, because we want parallel rays. So the lens is at a distance 50mm (approx) from the led. However, 50mm is too much distance for our design, so the question is...
  16. B

    I How to calculate the focal length and focal point of collimator?

    I wanted to calculate the focal length and focal point of the collimator. The collimator diameter is 3mm, and I wanted to focus on the 100-micrometre active area of the detector.
  17. S

    How to find the focal length of a lens (Problem with a task)

    Hello. I need formulas for the focal length of a lens when I have refractive indices of two centers and two radii of curvature of spherical surfaces or one radius of curvature of spherical surfaces. I search the internet but can't find it.
  18. S

    Uncertainty in the measurement of the focal length in this experiment

    ##\frac{1}{f}=\frac{1}{u}+\frac{1}{v}## ##f = \frac{u.v}{u+v}## Let: u + v = w → w = 250 mm ± 8 mm Percentage uncertainy of v = (3/50) . 100% = 6% Percentage uncertainty of u = (5/200) . 100%=2.5% Percentage uncertainty of w = (8/250) . 100% = 3.2% Percentage uncertainty of f = 6 % + 2.5 %...
  19. K

    Calculate the focal distance of the duplicate

    The picture below shows a so-called chromatic doublet, which is designed to minimize chromatic aberration, ie the wavelength dependence of the refractive index of the glass. The first lens has a flat first surface and a concave second surface with radius of curvature R and index of refraction n1...
  20. C

    Optics focal length and optical power Question

    1/f = 1/dₒ + 1/dᵢ = 1/1.0 + 1/0.33 = 4.03 m (focal length) Power: 1/4.03 m or 0.248 (0.25) *around to the2 decimal points? or leave it as a fraction? ((Did I do this correctly? I am not sure if this is correct and is it okay to be in meters not centimeters?)) Please let me know!
  21. O

    Diffraction pattern due to a lens with focal length f

    Suppose one light up with a laser on a grid with grid constant g. The grating is followed by a focusing lens with a focal length of f. In the focus (or immediately in front of it) the maxima have a distance d. How large was the distance of the maxima immediately after the grating? scheme: Laser...
  22. B

    Propagation of Error for Focal Length

    Homework Statement: Propagation of Error for Focal Length Homework Equations: f = (s'*s) / (s' + s) In my lab, we had to calculate the focal length of a lens based on object distances (s) and image distances (s') that we measured. The object distances were measured with an uncertainty of...
  23. fernelau

    Understanding the Impact of Convex Lens Focal Length on Water Temperature

    Summary: Hi, I'm doing an assessment for Physics on Optics topics, but I can't really explain how the CV affect the RV CV : Focal length of convex lens RV : Temperature of water after 20 minutes under the sun How I should explain for the temperature difference? 🤔 Please help, Thanks.
  24. F

    I Human eye and its focal length range....

    Hello, The human eye has an average diameter of ##2.5 cm## and an optical power between ##60D## and ##64D##. An object can be brought as close as the near point which is about ##25 cm##. If ##d_{o}=0.25m## (object distance) and ##d_{i}= 0.025m## (distance to the retina), the optical power...
  25. 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?
  26. S

    A Focal length and focus point

    First of all, Let me present some of the things I found from research. (considering convex lens) Interpretation 1 => Focal length is the distance from the center of the lens to the point where all rays converge. Interpretation2 => Focal length is the distance from the point of convergence to...
  27. G

    Calculate the focal length of the spectacle lens

    Homework Statement A hyperopic eye has a near point of 1.10 m. Calculate the focal length of the spectacle lens required to correct the hyperopia (assume that the near point of the normal eye is 25.0 cm.) Homework Equations 1/f=1/p+1/q The Attempt at a Solution I just used .25 m as p and...
  28. N

    Image with an Plano-Convex lens

    Homework Statement This isn't really a homework, but I am trying to figure out how this would work. I have an plano-convex lens with an focal length of 500 mm. I have an laser source that I like to focus on, to the infinity. I.e. I like to see the laser lobe. Case: What happens to image of...
  29. TheSodesa

    The focal length of a microscope eyepiece

    The question: -------------------- The length of a microscope pipe is $L=160\,\rm mm$, the transverse magnification of its objective $M_o = 40\times$ and the diameter $d_o = 5\,\rm mm$. As for the ocular/eyepiece, its magnification is $M_e = 10\times$. 1. Find out the focal length of the...
  30. Phil123

    [LENS] Given focal length and height, find object distance

    Homework Statement An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m? Homework Equations M = Yi/Yo = q/p...
  31. T

    Wave Physics - Optics - Effective Focal Length

    So we have the focal lengths: f1, f2, ..., f7 = 25mm And the distance between the lenses: d1-2, d2-3, ..., d6-7 = 50mm I have figured out that if the system would be afocal if it had an even number of these lenses. This is because the focal length of two adjacent lenses is the same as the...
  32. A

    Focal Length of Eyepiece

    Homework Statement The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.75 mm. What is the focal length of an eyepiece lens that will provide an overall magnification of -125? Assume student's near-point distance is N=25cm. Homework Equations...
  33. N

    About a concave mirror with a large focal length (1000mm)

    I have a Cassini PM-160 spherical mirror used in telescopes as the primary mirror. The mirror is concave with a radius of curvature of 2600mm and focal length of 1300mm. I have a very basic question. If an on object is located beyond the focal length of a concave mirror then the virtual image...
  34. P

    Focal Length given M and distance between obj and img

    Homework Statement The distance between an object and its upright image is 28.0 cm. If the magnification is 0.550, what is the focal length of the lens that is being used to form the image? Homework Equations 1/f = 1/so + 1/si M= -si/so The Attempt at a Solution See included image...
  35. W

    Understanding Two Convex Lenses: Ray Diagram and Focal Lengths

    Homework Statement I'm supposed to make a ray diagram of two convex lenses when light initially hits the first lens at parallel rays. When f(total) goes to infinity, the distance between the two lenses = the sum of the focal lengths of each lens. Homework Equations The Attempt at a Solution...
  36. N

    Focal Length

    Homework Statement 1) A double convex thin lens has a radius of 25 cm for the first surface and a radius of 40 cm for the second surface. If the glass has a refractive index of 1.55 the focal length is a) 28 cm, b) 9.93 cm, c) 121 cm, or d) 63 cm. 2) An object is placed 16 cm in front of a...
  37. Q

    Creating a two lens system of tunable focal length

    Hello, I would like to reduce the beam size of a laser by a factor of 10, with the purpose of replacing a long (750 mm) lens with a more compact design. Ideally I'd make a Galilean lens pair where the ratio of the focal lengths are 10:1 to produce a small collimated beam. However, I think I...
  38. M

    I Determining Appropriate Focal Length

    So I'm working on a project where we're deciding a new lens to use for our laser diode. I need to determine the appropriate focal length based on the equation: 1/ƒ = 1/μ + 1/σ where ƒ is our focal length, μ is the distance from the lens to image and σ is distance from lens to object. For the...
  39. P

    Plano convex lenses and focal length

    Does the orientation of a plan convex lens affect it's focal lenght? If I put il like in the first example in the photo and makeep the calculation using the lens maker equation I get f positive What happens if I turn the curved face on the right? Using the lens maker equation now the radius...
  40. N

    External focus in an optical system

    I feel a bit stuid for asking this. I have an optical system conisting of a laser source, a lens with some focal length F and aperture stop `(with some diamater D), followed by another lens (with another focal length) f and aperture stop d at some distance r from the first aperture stop D. What...
  41. R

    Stargazing Formulas for camera obscura (correct sub forum?)

    Experiment / demonstration: Set up military surplus command tent as camera obscura / pinhole projector for observation of full soar eclipse. Problem: lacking in personal knowledge of the formula needed to determine correct focal length to hole diameter Solution: Request assistance from actual...
  42. R

    Experimentally finding focal length of small biconvex lens?

    I have fabricated a few biconvex lens (12mm diameter) for an experiment and am trying to find their focal lengths. My though is to set up three parallel lasers and find where the beams converge. However, even with the smallest laser diodes I could find, three beams surpass the diameter of the...
  43. T

    Experiment: Measuring the focal length of a converging lens

    Homework Statement You are required to set up a light source, an object grid, a converging lens and a screen so that a quantitative investigation of object and image distances can be performed. Tabulate corresponding object and image distances (p and p' respectively). Also tabulate values of...
  44. G

    Calculate the focal length of a planoconvex lens?

    Homework Statement Calculate the focal length of a planoconvex lens that produces a real image 2.5 times as big as the object if the object is 2.5 cm from the lens? Homework Equations The only one I can think of is 1/f = 1/v + 1/u The Attempt at a Solution [/B] My 'attempt' is 1/f = 1/62.5...
  45. J

    B Variable focal length TV / screen

    Recently I have had a lot of eye strain from excessive computer use. The problem is because your eye lenses re stuck in a fixed position. I wanted to know if it would be possible to make a screen that is 1m away look like it is 4m away for example. Would it be possible by making the screen out...
  46. K

    Is it possible to magnify with a focal length of zero?

    Is it possible to magnify an object if the magnifier is sitting directly on top of the object (a focal length of zero)? How can this be accomplished if it is not possible with a traditional magnifier?
  47. RabbitWho

    Finding distance of image from mirror given focal length

    Homework Statement An object is at a very large distance from a concave mirror of focal length 40cm. Find the distance from the image to the mirror. Is the image real or virtual? Homework Equations 1/u + 1/v = 1/f The Attempt at a Solution [/B] 1/u + 1/v = 1/40 The image has to be real...
  48. M

    Stargazing Telescope Design: Calculating Total Distance from Primary Mirror to Eyepiece

    I am currently in the middle of constructing a Newtonian reflecting telescope and I had a question. The focal length for my primary mirror is 1500mm and 3mm for my eyepiece. My question relates to the path of the light inside the tube of a telescope. I understand that in a Newtonian reflector...
  49. F

    Calculating focal length from a number of focal ratios

    Homework Statement A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam...
  50. Alex_Neof

    Determining the focal length of a compound lens

    Homework Statement A biconvex lens, L_1, with focal length of magnitude \left| f_1 \right| = 15 cm is used with a second biconvex lens, L_2, with focal length of magnitude \left| f_2 \right| = 25 cm to form a compound lens system. If the two lenses are placed in mutual contact what is...
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