# Focusing Light

#### tommyers

Hi,

If I have a diverging light source, incident on a biconvex lens used for focusing the beam to a point.

How would one calculate the optimum distance between the lens and the beam source for optimum focusing? May question arises because I would expect the lens to be more efficient at focusing if the diverging beam covered the entire surface area of lens as opposed to a small spot on the lens surface, as would be the case if the source and lens were moved closer together.

Obviously, if the diverging beam spread the entire surface area and more, then optical power would be lost, right?

Regards,
Tom

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#### Andy Resnick

Expanding the beam to 'fill the entrance pupil' (the beam illuminates the whole lens) will allow use of the full numerical aperture of the lens- this will enable the tightest focusing (aberrations/misalignment = YMMV).

You should also collimate the incident beam as best as possible- the reason is (again) abberatons.

#### tommyers

You should also collimate the incident beam as best as possible- the reason is (again) abberatons.
Do you mean to use a collimating lens?

My light source has a divergence angle of 5 deg, and I wanted to use a biconvex lens to act as a condenser to focus the beam to a point.

I was hoping not to have to use a collimating lens due to the low cost nature of the application.

Regards,
Tom

#### ponjavic

Do you mean to use a collimating lens?

My light source has a divergence angle of 5 deg, and I wanted to use a biconvex lens to act as a condenser to focus the beam to a point.

I was hoping not to have to use a collimating lens due to the low cost nature of the application.

Regards,
Tom
Placing the biconvex lens it's focal length away from the source will collimate the beam. If you're lucky enough the resulting beam will have a diameter close to whatever aperture you're trying to fill. Otherwise you will have to get a second lens to make a beam expander/collimator.

Edit:
I just re-read it. Yes you will need another lens for the collimation. Possibly two lenses to get the beam to the right size to fill the focusing lens.
Another option is to just use an aspheric lens which always focuses light at a point but this would be much more expensive.

#### tommyers

OK, so I have my diverging source. One biconvex lens will collimate the diverging beam, another biconvex lens will take the collimated beam and focus it at its focal length?

Two asides:

1) If my assumption above is correct, then between the two biconvex lens (where the beam is collimated) I could use a filter which relies on a collimated beam? (whose incidence angle is 0 deg)?

2) How does the intensity of the beam increase when focused to a point?

Regards,
Tom

#### ponjavic

OK, so I have my diverging source. One biconvex lens will collimate the diverging beam, another biconvex lens will take the collimated beam and focus it at its focal length?

Two asides:

1) If my assumption above is correct, then between the two biconvex lens (where the beam is collimated) I could use a filter which relies on a collimated beam? (whose incidence angle is 0 deg)?

2) How does the intensity of the beam increase when focused to a point?

Regards,
Tom
Your assumption is correct but as Andy mentioned you need to be aware of aberrations unless the beam fills the entire lens (reason why you might want to have a beam expander/collimator using two lenses instead of one).

1) is correct

2) instead of having a beam radius of say a couple of millimetres you will have a diffraction limited beam radius (ignoring aberrations and other optical effects) which will be on the order of nanometres. As such your intensity/unit area (or volume) will increase between a thousand- and a million-fold

Its not a matter of distance between the lens and the beam, it’s the distance between the lens and the desired focal point. If it’s a biconvex lens it can be calculated like this.
Lensmaker's equation
The focal length of a lens in air can be calculated from the lensmaker's equation

1 1 1 (n-1)d
--=(n-1)[-- - -- + -----
f R R nR R
1 2 1 2

where

f Is the distance between the focal point and the lens,
n is the refractive index of the lens,
R is the radius of curvature of the lens surface closest to the light source,
1
R is the radius of curvature of the lens surface farthest from the light source and,
2
d is the thickness of the lens (the distance along the lens axis between the two surfaces vertices

I’m going to assume your trying to fathom a laser type situation if so you might find spherical aberration helpful.

#### tommyers

I do not understand threadmark's equation / diagram?

It has been jumbled in the browser,Food for research. try bifocals.

#### samsha

Hi friends I am new to PF . I want to collect a distant light spot ( 30 meters away) using a collimator and then through fiber spectrometer I want to analyse it. Please suggest me how I can make the collimator

#### Andy Resnick

If you are talking about visible spectroscopy, and the source really is 30 m away, the light at basically already collimated- as far as your lens is concerned, the source is at inifinity. A simple plano convex lens (the larger the diameter, the more light you will collect) used at an f-number matched to the acceptance angle of the fiber is the most simple solution.

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