Difference between focal length and the distance from the lens

[greener1993]

Lens and distances

I do use images as help when working theses out. going to try and scan theses in but tryed my best just using pc for now. 0 = lens F = focal length

1) a camera with a 50mm focal length lens is focused on a persons face 1m from the lense. show that the film will be about 53mm behide the lens.
(focal length = 0.05)
------------------0--F--------------
(-) (?) (1m) (+)

Simple knowledge says 1/v=1/u +1/f i then rearranged that to make 1/u=1/1 - 1/ 0.050

= 20... not 53 mm, very confused :S

2) with a zoom lens you can vary the power of a lens. show that a lens power of about 24 dioptre is required to focus a flower that is 250mm in front of the lens on a piece of film that is 50 mm behide the lens.

im extremely confused on this one. I yet again used 1/v=1/u+1/f rearranged it to make 1/u = 1/v - 1/f or 1/u= 1/0.25 - 1/24 = 3.95 :S not 50

I would think I've just messed up the equation in this one.

3)A lamp 400mm from a lens is in focus on a screen 400mm from the lens on the other side of the lens. show that the lens has a power of 5 diopters and a focal lenth of 200mm. Explain why the lamp must be moved nearer to the lens to project its image further away.

im unable to find out how they got 200mm focal lenth from there i can work out the power. 1/0.2 = 5. the wording of this question is extremely bad.

additional help

Just a couple of quick question that arnt on my homework but would like to know for background info.

whats the difference between focal lenth and the distance from the lens and why are they so different? what happens if it is not the same as the focal lenth? it is burred?


Cheers people, Thanks for looking

P.S sorry for bad spelling i have dyslexia:)

 

[Delphi51]

1/u=1/1 - 1/ 0.050

Put all distances in the same units. Are you sure about that formula? I seem to remember 1/Di + 1/Do = 1/f where Di is the distance from the lens to the image, Do is the distance from the object to the lens and f is the focal length.

Better look up "dioptre" for #2. You haven't used it correctly.

#3 looks clear to me. Same formula.

 

[kerimek]

I would like to clarify the difference between focal length and the distance from the lens. Focal length is a property of the lens itself and is defined as the distance between the lens and the point where the light rays converge to form a sharp image. It is usually measured in millimeters (mm). On the other hand, the distance from the lens refers to the actual physical distance between the lens and the object or subject being photographed. This distance can vary depending on the position of the object or subject relative to the lens.

In the first question, the film will be about 53mm behind the lens because the focal length of the lens is 50mm and the object is 1m away from the lens. Using the equation 1/v=1/u+1/f, we can calculate the image distance (v) by substituting 1m for the object distance (u) and 50mm for the focal length (f). The result is v=53mm, which means the film will be 53mm behind the lens.

In the second question, the lens power is given in diopters, which is a unit used to measure the optical power of a lens. The equation you used, 1/v=1/u+1/f, is not applicable in this case because it is for thin lenses. For thick lenses, we use a different equation, (n-1)(1/R1+1/R2)=1/f, where n is the refractive index of the lens material, R1 and R2 are the radii of curvature of the lens surfaces, and f is the focal length. Using this equation, we can calculate the required lens power to be 24 diopters.

In the third question, the lens has a power of 5 diopters and a focal length of 200mm. This means that the lens has a curvature that bends light rays to a certain degree, resulting in a focal length of 200mm. The lamp must be moved closer to the lens to project its image further away because the closer the object is to the lens, the larger the image will be. This is due to the fact that the light rays coming from the object will converge more strongly, resulting in a larger image on the screen.

To answer your additional questions, the focal length and the distance from the lens are different because they measure different things. The focal length is a property of the lens itself, while