What is Focal length: Definition and 236 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. 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...
  2. D

    Finding the Focal Length: A Homework Challenge

    Homework Statement Homework Equations 1/do+1/di=1/f The Attempt at a Solution I tried finding the distance of image at 27m and then at 30.5m and taking the difference but that didn't work.
  3. W

    Deriving back focal length using Fermat's principle

    Homework Statement The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length Homework Equations N/A The Attempt at a Solution I've...
  4. F

    Thick Lens focal length and surface facing the object

    Hello Forum, In the case of an ideal, thin lens (free from any aberration), it does not matter which face of the lens is facing the object. The results will be identical. What if the lens was an ideal (no aberration) thick less with the H planes, etc...? Would it matter which lens surface is...
  5. vetgirl1990

    What is the relationship between focal length and focal points?

    Homework Statement This is a silly question... but I know that a lens has two focal points but one focal length. If each focal point is at 5cm from the lens, would the focal length be 5cm, or 10cm (adding the position of each focal point together)? Homework Equations N/A The Attempt at a...
  6. Alettix

    Measurement of Focal length with Laser beam

    Homework Statement Hi! I have lately come across some tricky experimental physics tasks, where no solution is given. Some of them involved parts where the focal length of a convex lens had to be measured with a laser. How do you do this? Homework Equations 1/l + 1/d = 1/f (1) where f is the...
  7. K

    Can you find lens magnification from focal length?

    If you know the focal length of a lens and use the lens equation 1/do + 1/di = 1/f by assigning some arbitrary do and solve for di, can you then find the magnification just from the focal length from -di/do?
  8. R

    What is the speed of sprinter running away from lens?

    Firsts of this is not my problem I don't even take physics but it is my girlfriends. She doesn't know how to get the answer an neither do I. I took some physics but not enough for this. 1. Homework Statement A sports photographer has a 160-mm-focal-length lens on his camera. The photographer...
  9. M

    Focal length of diffraction grating for recip. dispersion

    Homework Statement What would the focal length be of a diffraction grating if the set up is a laser placed 1 m from the 0 order diffraction? Would it be the distance from the grating to the laser or the distance from the grating to the image? Homework Equations 1/f = 1/o + 1/i Rd = [Df]-1...
  10. M

    Find Magnification of Reflecting Telescope

    Homework Statement Find the magnification of a 10" reflecting telescope with a focal length of 1250mm and a 250mm eyepiece. Homework Equations 1/f=1/do+1/di M=hi/ho=-di/do The Attempt at a Solution Not really sure where to start. If you could, please explain how you got the answer. Thanks for...
  11. Siddharth Venu

    Convex Lens Problem: Find Focal Length

    A screen is placed 90cm from a object. The image of the object on the screen is formed by a convex lens at two different locations separated by 30cm. The focal length of the lens is what?
  12. Kompewt

    Focal length of thin converging lens

    Homework Statement An outdoor security camera has a simple lens with focal object length fo = 6.00 cm and perfectly focuses the image of a bird onto its detector located 9.00 cm away from the lens. The animal then flies away from the lens and the new focal distance is 8.00 cm. (a) How far did...
  13. P

    Equivalent focal length of two lenses

    Homework Statement Two thin lenses have focal lengths of -5cm and +20cm. Determine their equivalent focal lengths when (a) cemented together and (b) separated by 10cm. Homework Equations ##\frac{1}{f_{eq}}=\sum_{n=1}^k \frac{1}{f_n}## The Attempt at a Solution So the first part was easy since...
  14. D

    Focal length of magnifying glass for VR?

    Hi the standard focal distance seems to be 45mm for vr headsets such as google cardboard. In other words there's a pair of convex lenses in front of your eyes with the screen being 45mm away from the lenses ... I am not sure why you can't use different lenses to reduce the focal distance to the...
  15. B

    Understanding the Human Eye: Exploring Focal Length and Retinal Distance

    I never could understand this: the lens focuses light onto the retina so shouldn't the distance between the lens and the retina be the focal distance? It does not seem to be the case while I was trying to look around for the answer on the internet. And since light is focused on the retina, the...
  16. M

    Focal length of lens at border of two liquids

    Homework Statement I need to find optical power (reciprocal focal length) of this system with thin lens Homework Equations I tried to solve this using spherical diopter equation n1/a+n2/b=(n2-n1)/R where a is object distance and b is image distance The Attempt at a Solution equation for...
  17. S

    Calculating Focal Length of 1D Fresnel Lens

    Homework Statement Calculate the focal length of 1D Fresnel lens, whose transmittance is given as $$T(\xi)=\frac 1 2(1+\cos(\alpha \xi ^2)).$$ Homework Equations Anything you wish The Attempt at a Solution I have no idea. I tried to use the equation for diffraction image $$u_p=C\int _0...
  18. M

    Determining the focal length of a gradient index lens

    Homework Statement There are three subquestions in this question, all marked bold. Let's consider a gradient index lens of thickness ##d##, whose refractive index changes with the distance from the axis with the following formula $$ n(r) = n_1 + a r^2 $$. Determine the lens's focal length...
  19. B

    Distance from the object to objective lens and focal length

    Homework Statement 1) The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.70mm . If this lens produces a lateral magnification of -42.5, what is its "working distance"; that is, what is the distance from the object to the objective lens? 2) What is the...
  20. S

    Calculating the distance between the optical center and focal length

    -Hello everyone. At school, I studied about convex lense and concave lense. They are very interesting, we learned about how lights would be after going through the lense. But what I want to ask is how we can calculate the distance between optical center and focal (I means focal length). Focal...
  21. R

    Focal length of 2 lenses to reduce laser beam diameter

    I need to reduce the beam diameter of a laser I am using. I plan to do this by first passing the beam through a positive spherical lens with focal length f1 and then a negative spherical lens with focal length f2 and f2 < f1. By placing the lenses so that the two focal points overlap I will have...
  22. Robsta

    Calculate focal length of lens by diffraction.

    Homework Statement A collimated beam from a white-light source is incident normally on a transmission grating with 500 lines per mm. The transmitted light then passes through a lens which is used to project the visible (380–780 nm) spectrum of the light source on to a strip of photographic film...
  23. A

    Focal length of a distorted window

    Homework Statement What is the focal length of a dewar window distorted by a pressure difference? As a result of the pressure difference, the radius of the first surface of the window is R1 = 100 meters. The window is 3 mm thick, with an index n = 4 at l = 4 um. Homework Equations I think I...
  24. Prashasti

    Finding Focus Length in Broken Double Convex Lens

    Homework Statement A thin double convex lens of focal length f is broken down into two halves at the axis. The two haves are then combined, as shown in the figure. What will be the focal length for the arrangements...
  25. R

    Focal length of the optical system

    I understand this that when an object is kept at focus of convex lens, then image is formed at infinity. So when we keep a convex lens above plain mirror and move object needle on the principal axis of convex lens and see a coinciding image with needle on lens and measure distance from lens then...
  26. S

    Focal length to get clear image

    Homework Statement Harris stands at point A and wants to take a picture of bird located at point B. Because there is wall, he has to direct his camera to mirror located 3.7 m to the north from his position. What is the focal length of his camera so that he can take a clear picture of the...
  27. 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...
  28. C

    Focal Length Problem: -30cm Converging/Diverging Lens

    Homework Statement A lens made of glass has one concave side with a radius of curvature of 5 cm, and one convex side with a raduis of curvature of 7.5 cm. What is the focal length of the lens? Is this a converging or diverging lens? Homework Equations nglass=1.5 nair=1.0...
  29. P

    How is the focal length of an objective calculated?

    Hi, I am using an objective lens to illuminate my object by a collimated beam. The magnification and NA is available on the objective. How can I calculate the focal length from this information? The objective is not infinity corrected. Thank you
  30. H

    Focal Length of a Plane Glass: How to Measure and Understand Its Infinite Power

    Homework Statement what is the focal length of a plane glass ? Homework EquationsThe Attempt at a Solution place a plane glass in a plane and allow light to pass through it measure its focal length (i think its focal length is infinite )
  31. K

    Finding the focal length of a negative lens without another lens.

    Homework Statement A simple method for determining the focal length of a negative lens is shown below. Prove this is true. Homework Equations The Attempt at a Solution The linear magnification formula relates magnification, the distance from the lens to the image (i), the distance from...
  32. D

    How Do You Calculate the Focal Length of a Telescope's Objective?

    Homework Statement An optical telescope with a 12mm eyepiece makes the Moon appear to have an angular diameter of 30 degrees. What is the focal length of the telescope's objective? Homework Equations magnification=focal length of objective/focal length of eyepiece The Attempt at a...
  33. D

    Focal length of combined glass lens and water lens

    Homework Statement please refer to the photo, Homework Equations The Attempt at a Solution why can't I directly use the lens maker formula to get the ans ? my working is 1/f = ( (1.5-1.33) /1.33) x ( (1/20) + 0 ) ...finally , i get my f = -160cm. the radius of curvature of...
  34. E

    Focal length of converging meniscus lens filled with a liquid

    Homework Statement A converging meniscus lens is made of glass with index of refraction n = 1.55, and its sides have radii of curvature of 4.5 cm and 9 cm. The concave surface is placed upward and filled with carbon tetrachloride which has index of refraction n' = 1.46. Determine the focal...
  35. A

    Measuring the focal length of a deformable lens

    Hello all, My lab recently purchased a deformable lens, which can change its focal length from 140 mm to 40 mm and anywhere in between, based on current applied to it. I'm wondering how to use a beam profiling camera to measure the focal length of this lens at various current levels. We...
  36. M

    Focal length of a sphere with refractive index gradient

    Homework Statement We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function. Homework Equations Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length. The Attempt at a Solution I...
  37. T

    Focal length short and long. Which to choose?

    I'm building a telescope and one of the more important choices I'm making is what focal length to make the mirror, my understanding is the longer the focal length the closer you see far away stuff, but the field of view diminishes a bunch. I've seen both long tube dobsonians and short tube ones...
  38. B

    Focal Length of a Plano Convex Lens

    Hi, The focal length of the Plano-Convex lens as calculated by the lens maker equation: Does it work when light crosses the lens from the convex side, planar side, or both? Thanks.
  39. N

    Moving an object and screen to find the focal length of a lens

    Homework Statement A convex lens is used to project the image of an object on a screen with a magnification m1 . Leaving the lens fixed, the object is moved along the optical axis by a distance Δs and the screen is moved until the image is located again. If the new value of the...
  40. X

    Optics: Focal length of Koenig eyepiece

    Homework Statement A Koenig eyepiece with a focal length of 100mm is constructed in the following way: The first lens is made of 755276 glass which is 10 mm thick on axis. The radius of curvature of its left hand surface is -225mm, the radius of curvature of it right hand surface is 83.6...
  41. L

    Analyzing Two Converging Lenses of the Same Focal Length

    Homework Statement Two converging lenses of the same focal length f are separated by distance 2f. The axis of the second lens is inclined at angle θ = 60º with respect to the axis of the first lens. A parallel paraxial beam of light is incident from left side of the lens. Then: (A)...
  42. U

    Diffraction Grating, focal length of lens

    Homework Statement Light from infinity strikes a diffracting grating normally with 600 lines per mm. The emitted light then passes through a lens to project visible light (400-800 nm) spectrum onto a screen that is 50mm, just enough to cover it. Find the focal length of the lens. Homework...
  43. S

    From what point is the focal length of a thick lens measured?

    I'm designing an eyepiece for fun and want to be accurate. I just realized my physics book equations are approximated for thin lenses only. Suppose I have a convex convex lens or a plano convex lens, lateral parallel rays coming from one side or the other, and a focal point on the opposite...
  44. A

    Focal length of a convex mirror

    Homework Statement An object is 12.0 cm in front of a convex mirror. When the convex mirror is replaced with a flat mirror, the image distance is 5.0 cm farther away from the mirror. What is the focal length of the convex mirror? Homework Equations f=-1/2R 1/do+1/di=1/f The...
  45. A

    How Is the Focal Length of a Mirror Determined When the Image Size Doubles?

    Homework Statement The image of an object seen in a mirror is twice its actual size. The orientation of the image is the same as that of the object. If the object distance do is 1.7 m, what is the focal length of the mirror? Homework Equations 1/do+1/di=1/f m=-di/do The Attempt...
  46. T

    Camera Specifications computing focal length and f/#

    So I have come across a specification of a narrow field of view camera. The specification states IFOV=30 microrad FOV=2x2 resolution=<.1m at 1 km If I assume a 1K sensor at 9micron pitch and an aperture = 3.7cm I have resolution at .013 m Chip size = 9.2mm Focal length is...
  47. P

    How does the index of a medium affect the focal length of a lens?

    Homework Statement Suppose we have a lens of known focal length, f=100 cm. (a) If light enters the lens from air, but after the lens enters a medium with index 1.33, how far from the lens will focus? (Assume the incident light is collimated.) (b) What if there is instead air after the lens...
  48. A

    Focal length multiplied by wavelength

    Simple question: is there any physical significance of the quantity (focal length of lens)*(wavelength of laser light passing through the lens) ? How does it relate to the size of an image on the image plane? According to my professor, (focal length)*(wavelength)/(constant) is the length of...
  49. A

    Find the Focal Length Of a lens

    Homework Statement When an object is placed 69.0cm from a certain converging lens, it forms a real image. When the object is moved to 39.0cm from the lens, the image moves 19.0cm farther from the lens. Find the focal length of this lens. Homework Equations 1/do + 1/di = 1/fThe Attempt at a...
  50. C

    Compound microscope focal length

    Homework Statement The barrel of a compound microscope is 15 cm in length (distance between lenses). The specimen will be mounted 1.0 cm from the objective, and the eyepiece has a 5.0-cm focal length. Determine the focal length of the objective lens. Known: f2=5cm, L=15cm, do1=1cm...
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