Lenses And Simple Optics



Lenses

Lenses are one of the most important devices in optics. Lenses are used is many applications requiring the manipulation of light waves.

Lenses work by refractinglight waves in a particular manner denoted by the construction of the lens itself. Different type of lenses will either refract light to a point, called a Focus Point, or they may cause the light waves to diverge outwards.

One of the most common lens is the Plano - Convex lens, this lens has one side which is flat, and the other side which is curved like a sphere. This type of lens is thicker at the centre than the edges - a positive lens.
 

Lens Types Diagram.  Flavio Spedalieri

Fig 2.2

Fig 2.2. shows the six primary types of lens used in optics. the lenses are further sorted into NEGATIVE lenses and POSITIVE lenses.
 

Positive Lenses

Positive lenses are lenses which are thicker at the centre than at the edge. The combined effect of refraction at the front and back surfaces of the lens  will bend light to a point or Focus - The light from this type of lens is focused to a point IN FRONT of the lens.

Positive lenses produce a REAL IMAGE, -  the image produced by this type of lens CAN be projected onto a screen.

The three basic positive lenses are:

Double Convex lens
Plano - Convex lens
Positive Meniscus lens

 

Convex Lens Diagram.  Flavio Spedalieri

Fig 2.3

Fig 2.3 shows some important aspect of a positive lens, and its behaviour on light.
 

Negative Lenses

Negative  lenses are lenses which are thinner at the centre than the edge. The same optic laws apply to negative lenses as they do with positive lenses, but a negative lens works in a somewhat different way than a positive lens.

The focal lengths of this type of lens are negative, this can be worked out mathematically by assigning a negative radii of curvature  to a concave lens surface. If you pass parallel light rays through a negative lens, they seem to spread out  from a point behind the lens, the distance from this point to the centre line of the lens is the focal length; this is given a negative value, as it is on the opposite side of the lens from the focal point of a positive lens.

Because negative lenses do not bring parallel light rays together, they DO NOT produce a real image, but they do produce a VIRTUAL IMAGE.

The three basic negative lenses are:

Double Concave lens
Plano - Concave lens
Negative Meniscus lens

 

Concave Lense Diagram.  Flavio Spedalieri

Fig 2.4

Fig 2.4 shows some of the important aspects of a negative lens, as you can see, a negative lens produces a virtual image, and the focal point is behind the lens.


Other Lenses And Aberration

There are many variations on lenses and design. An important factor with lenses that can cause problems is Lens aberration. When dealing with the conceptual scientific principles, discussions are based around 'Ideal' 'perfect' model scenarios. In the real world, the 'ideal' models are non-existent due to physical properties and variables which play a part.

When dealing with lenses, the basic materials from which they are made have variations which have an effect on the way light behaves, these mainly related to refractive index and dispersion of the glass. Dispersion is the change of index of refraction with wavelength.

As we studied previously, white light is made up of many colours or wavelengths. Red light (long wavelength) has less energy than Blue light (short wavelength), and therefore when passing through a medium, the refractive index will cause the light waves to slow down, Red is bent or refracted the least, and blue is refracted the most.

When light passes through a lens, refraction of light will occur. When dealing with the Ideal single convex lens model, we know that light rays are focused to a finite point. In reality due to refraction and dispersion, the lens will not be able to focus the different wavelengths at the exact same point as the focal point is dependant on refraction and the index of refraction of the lens.

This type of effect is known as 'Chromatic Lens Aberration' The result of chromatic aberration is the image produced by the lens will have a coloured boundary, and will appear blurry

Another type of lens aberration is known as spherical aberration. As lenses are made with spherical surfaces light rays that are parallel but at different distances from the optical axis, will fail to converge at the same point.

Lens Aberration Diagram.  Flavio Spedalieri

Fig 2.5

Fig 2.5 shows the details of chromatic and spherical aberration. There are other forms of aberration such as astigmatism and distortion. All forms of aberrations will cause a decrease in quality of the resolved image.

The effects of aberration can be corrected by utilising multiple lens systems known as compound lenses. Compound lens systems are widely used to yield long and short focal lengths and or high magnification.

Another type of lens is the Graded Index (GRIN) lens and the spherical lens. These lenses are made using materials with varied refractive indexes. Such lenses are used to couple light sources into very small apertures such a optical fibres.