# Focal length Definition and 26 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. ### 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.
2. ### 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...
3. ### 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...
4. ### 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.
5. ### 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...
6. ### 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?
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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...
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### 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...
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### Two Convex Lenses

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...
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### 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...
15. ### 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...
16. ### 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...
17. ### Stargazing Telescope Design

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...
18. ### 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...
19. ### 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...
20. ### 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...
21. ### Convex lens problem

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?
22. ### 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...
23. ### 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...
24. ### Convex lenses

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. ### 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
26. ### 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...