Peter's Physics Pages

An Introductory Physics Course with Peter Eyland
Lecture 9 (Optical instruments)

In this lecture the following are introduced:
• The Camera
• Aberrations in lenses
• Telescopes
• Binoculars
• Microscopes

The Camera

A simple camera has four parts. An aperture that restricts the angle and amount of light that can enter a light tight container. A lens to focus the scene. A shutter that is normally closed and momentarily open to allow light inside. A photographic film or Charged Coupled Device (CCD in "digital" cameras) to capture the image.

If the aperture is small enough, a camera doesn't need separate focussing for near and far objects. This is because rays from the same area of the picture only diverge a little from each other, even though they may come from different distances. They come together on a tiny area of the film (which can't record every detail) so the picture is reasonably clear. A small aperure thus has a good depth of field, because objects at quite different distances are all "in focus".

However a small aperture means there is only a small amount of light that can enter the camera body and it gives low illumination onto the film. A film is then needed which responds quickly (i.e. a "fast" film).

Cameras with larger apertures and lenses allow more light to enter and so are better in low light conditions, i.e. they can use "slower" films in normal lighting. However, they will also need a focussing mechanism and will have a smaller depth of field (objects at different distances can be blurred).

f-number

The f-number of a lens characterises the brightness of the image on the film. The f-number is the focal length of the lens divided by the diameter of the aperture of the lens.

Smaller f-numbers mean brighter images, because:
• The longer the focal length; the image is larger and dimmer.
• The bigger the diameter of the aperture; the more light is gathered.

A diaphragm (or iris) changes the aperture and allows the f-number to be changed for different light conditions. Since the area of light admitted changes with the square of the diameter, if the f-number is doubled then the exposure time needs to be multiplied by four.

Anti-reflection films

Lenses should not reflect the light that falls on them (it is needed inside!). Good lenses have an anti-reflecting film. These films use the property of wave interference to cancel out reflected waves from each side of the film. They can give the lens a "plum" colour (so don't try to rub it off).

Aberrations in lenses

The quality of the image that is formed in a camera depends on the quality of the lens system. A simple spherical lens cannot produce a flat sharp image of a scene that has colour, width and depth.

Chromatic aberration

A simple lens has different focal lengths for different colours. Incident white light parallel to the axis produces a longitudinal colour separation, (blue light is refracted more than red light).

The result of this is that an image will have blurred coloured edges. By using two kinds of glass (i.e. with different refactive indices) an acromatic doublet, can be made which makes the light recombine.

The lens in the human eye produces chromatic aberration. However a yellow pigment in the back of the eye, (which absorbs blue light) helps to minimise this aberration.

Spherical Aberration

The spherical shape of a lens causes monochromatic (single colour - here shown as red) rays near the edge to refract more than rays near the axis. Rays near the axis are called paraxial rays. The spherically aberrated image shows a point image as a blurred circle.

The Hubble Space Telescope initially had this problem because of a miscalculation. It was fixed later and now produces pictures such as this one from Warrick Couch when he was at UNSW. Note the arcs caused by the gravity of galaxies bending light around them (gravitational lensing).

and so to telescopes…

The Optical Telescope

Some optical telescopes are designed to take pictures of the night sky (photographic telescopes), others are designed for people to look through (visual telescopes). There are 2 main telescope forms, refracting (where lenses are used) and reflecting (where mirrors are used). Refracting telescopes include the Galilean telescope, the Keplerian telescope and Binoculars. There are a wide variety of reflecting telescopes.

Galilean Telescope

The first visual telescope was probably made in 1608, by a Dutch spectacle grinder named Hans Lippershey. It was popularised by Galileo and his version can be seen on exhibit in Firenze (Florence), Italy. It producess an upright image which is useful for applications such as "opera glasses".

It uses a convex (or "positive") lens for the objective and a concave (or "negative") lens for the ocular or "eye-piece". The focal plane of the objective and the eye-piece coincide.

The image is at "infinity", because the rays, which apparently come from the image, are parallel. Thus, the telescope is set up for "relaxed vision", where relaxed vision means you are gazing into the distance. The dotted green construction ray through the centre of the eye-piece lens is parallel to the central ray through the objective lens.

Magnification
The magnification of a telescope is the ratio of the angle to the image over the angle to the object. Finding a relationship for the magnification is a little tricky and the following diagram is an enlargement up of the Galilean telescope above but with unnecessary details omitted. FB is the dotted green construction ray.

There are three right angled trianges, ABC, CDF, and BEF. There is the length AB = fo - fe. Lengths EB = DC = fe. There are two "unknown" lengths FE and ED = BC (call them x and y). Take tan A, tan B, and tan C, substitute the "knowns", eliminate the "unknowns" using the first two equations , find the ratio of tan θ' to tan θ, and the following will result.

Build your own Galilean Telescope with this student project.

Keplerian telescope

The German astronomer Kepler (1571 - 1630) designed a telescope with two positive lenses.

Relaxed vision will occur when the focal planes of the objective and eye-piece are coincident. This produces images which are upside down; but in astronomy, it doesn't matter which way the image is oriented. The magnification is the same as in the Galilean telescope.

Viewing so that the image is at the distance of most distinct vision has the objective focal point just inside the eyepiece focal length.

Example
An astronomical telescope has two positive lenses for an angular magnification of 60x. Its eye-piece has a 20 mm focal length. Find the distance between the objective lens and the eye-piece.

Binoculars

Binoculars are twin telescopes. To reduce their length, they use prisms to (total internally) reflect light backwards and forwards.

Reflecting telescopes

There are lots of different designs,

here are some:
 Name Primary mirror Secondary mirror Comment Cassegrain concave parabolic convex hyperbolic folded path through hole in primary Gregorian concave parabolic concave ellipsoidal folded path, concave mirror gives upright image Schmidt concave spherical convex spherical aspheric aperture corrector lens, film at prime focus Schmidt-Cassegrain concave spherical convex spherical aspheric aperture corrector lens, folded path Maksutov concave spherical(or ellipsoidal) convex spherical(or hyperbolic) spherical corrector lens, folded path Newtonian concave parabolic plane diagonal plane mirror gives view on the side Wynne-Rosin concave parabolic convex spherical lens doublet near primary focus for chromatic corrections and increased field of view Dall-Kirkham concave ellipsoidal convex spherical folded path through hole in primary Ritchey-Chretien concave hyperbolic convex hyperbolic folded path through hole in primary Wolter grazing incidence on concentric paraboloidal - hyperboloidal surfaces X ray telescope

Here are a few ray diagrams:

Newtonian Reflector

Schmidt-Cassegrain

Ritchey-Chretien

This is the Parkes radio telescope that was used to bring TV pictures from the Moon. It focusses radio waves instead of light and so can be used in the daytime as well as night.

Microscopes

Microscopes are almost the same as Keplerian telescopes, the difference is that the focal lengths are in the opposite ratio. Keplerian telescopes have a long focal length objective and a shorter focal length eye-piece. Microscopes have a short focal length objective and a longer focal length eye-piece. Microscopes are set up to produce a final image at the distance of most distinct vision, which is about 250mm.

Modern microscopes usually have three lenses. Here are optical microscope images of bird feathers.

Example

A microscope has an objective focal length of 3mm and an eye-piece with focal length 12mm. The object is 3.5mm in front of the objective and the distance between the lenses is 33.5mm. If the final (virtual) image is 250mm from the eye-piece, find the magnification of the microscope.

The lens equation and the definition of (lateral) magnification are:

Using these symbols and d = distance between lenses:

Electron microscopes

An electron microscope uses a stream of electrons, which are bent in much the same way that light is refracted. Here are electron microscope pictures of viruses. Here are everyday insects from microangela. An atomic force microscope can image individual atoms.

Summarising:

A simple camera has four parts. An aperture that restricts the angle and amount of light that can enter a light tight container. A lens to focus the scene. A shutter that is normally closed and momentarily open to allow light inside. A photographic film or CCD to capture the image.
A small aperture gives good depth of field and a large aperture gives good illumination.
The f-number is the focal length divided by the aperture: smaller f-numbers mean brighter images.
A single spherical lens has chromatic and spherical aberration.
The Galilean telescope has a concave lens for the eye-piece and a convex lens for the objective.
The Keplerian telescope has two convex lenses and an inverted image.
The final image in either telescope is at infinity and the focal planes coincide. The magnification is the ratio of the objective focal length to the eyepiece focal length.
Binoculars are twin telescopes with prisms to reduce their length.
The Newtonian telescope has a paraboloidal primary mirror and a plane mirror to reflect off to the side.
Microscopes usually have three positive lenses and the final image is at 250mm.
Electron microscopes can image individual atoms.

email Write me a note if you found this useful