Fresnel Blender

How far is the image produced from the centre line of a convex lens if an object is placed 4cm away from this convex lens of focal length 8cm?

Georges-Louis Leclerc de Buffon (1748) originated the idea of dividing a lens surface into concentric rings in order to reduce the weight significantly. In 1821 this idea was adopted by Augustin-Jean Fresnel in the construction of lighthouse lenses.

Fresnel effect

`1/F=1/(d\o)+1/(d\i)``1/(10cm)=1/(30cm)+1/(d\i)``0.1=0.03dot3+1/(d\i)``0.1-0.03dot3=1/(d\i)``1/(d\i)=-0.06dot6`Multiply both sides by `d\i` and divide both sides by `0.06dot6` to get `di` on its own, we have:`1/(0.06dot6)=d\i``d\i=15cm`

Fresnel equation

We can see immediately that when the object is placed between the lens and `F` (the principal focal length) then the image is going to be:

Fresnel lens, succession of concentric rings, each consisting of an element of a simple lens, assembled in proper relationship on a flat surface to provide a short focal length. The Fresnel lens is used particularly in lighthouses and searchlights to concentrate the light into a relatively narrow beam. It would be almost impossible to make a large lighthouse lens of the usual solid glass-disk type because the thickness and weight would be prohibitive; the lighter Fresnel lens is constructed of elements that are separately ground and polished from suitable glass blanks and assembled to make up the complete lens.

An object 25cm away from a lens produces a focused image on a screen 15cm away. What is the focal length of the converging lens?

Fresnel pronunciation

A wide variety of thin Fresnel lenses are molded in plastic, the width of the rings being only a few thousandths of an inch, for use as field lenses with ground-glass screens in cameras and small projectors to increase the brightness of the outer parts of the screen.

Although this ray diagram sketch doesn't give us an exact answer we know that in order for an image to be created the object will be at the first set of numbers between 1 and 6 and the image will be on the other side of the lens again between 1 and 6.

Fresnel Light

A converging lens has a focal length of 10cm. If a light is located 30cm from the lens, what type of image will be formed and where will it be located?

Fresnel lens

A one-piece molded-glass Fresnel lens is convenient for spotlights, floodlights, railroad and traffic signals, and decorative lights in buildings. Cylindrical Fresnel lenses are used in shipboard lanterns to increase visibility.

We can see from this sketch that if the principal focal length is 10cm and the object is 30cm from the convex lens then the image will be further away than `2F` (see point 1, 2 or 3) and will be real and inverted.

but the image could be smaller or larger than the object. From the sketch we also know that `d\i` is +ve therefore using lens formula we get:

`1/F=1/(d\o)+1/(d\i)``1/8=1/4+1/(d\i)``0.125=0.25+1/(d\i)``0.125-0.25=1/(d\i)``1/(d\i)=-0.125`Multiply both sides by `d\i` and divide both sides by `-0.125` to get `di` on its own we have: