Seeing Things Through Lens Putting Lenses Together

Astronomical Telescope The simplest Astronomical Telescope consists of only two lens, an Objective and an Ocular lens.

Light rays coming from distant objects are essentially parallel. Astronomical Telescope

The only characteristic ray that can be used is the incident ray passing through the Optical Centre of the Objective lens. It does not refract and passes straight through. Astronomical Telescope

Since experimentally we know that an image is formed on the focal plane of the Objective lens…… Astronomical Telescope

Since experimentally we know that an image is formed on the focal plane of the Objective lens, all of the parallel light rays striking the Objective must focus and form an image on the focal plane. Astronomical Telescope

Also, Objective lenses with large diameters collect more light and produce brighter images. Astronomical Telescopes have Objective lenses with large diameters.

Astronomical Telescope The focal length of the Objective lens effects the size of the image.

Astronomical Telescope Long focal lengths form larger images. Astronomical Telescopes have Objective lenses with long focal lengths.

Astronomical Telescope Now for the Astronomical Telescope Note that the focal length of the Objective lens is not to scale. Parallel rays coming from a distant object……

Astronomical Telescope Now for the Astronomical Telescope Note that the focal length of the Objective lens is not to scale. Parallel rays coming from a distant object form a real image at the Focus of the Objective lens.

Astronomical Telescope The real image formed by the Objective lens acts like an object for the Ocular lens. An incident ray parallel to the principal axis refracts……

Astronomical Telescope The real image formed by the Objective lens acts like an object for the Ocular lens. An incident ray parallel to the principal axis refracts through the Ocular lens’ Focus.

Astronomical Telescope An incident ray coming from the same direction as the Ocular lens’ Focus refracts……

Astronomical Telescope An incident ray coming from the same direction as the Ocular lens’ Focus refracts parallel to the principal axis.

Astronomical Telescope An incident ray passing through the Optical Centre of Ocular lens……

Astronomical Telescope An incident ray passing through the Optical Centre of Ocular lens does not refract and passes straight through.

Astronomical Telescope The final image is where the rays refracted from the Ocular lens appear to come from. It is larger, inverted, and virtual.

Astronomical Telescope This is actually not the correct relationship between the two lenses. It was only drawn to show how the Objective lens’ image could be used as an object for the Ocular. The correct lens relations ship follows.

In order to understand the correct relationship between the two lenses, the human eye must be taken into account.

The human eye is made up of several parts. Focal length mm Brain Optic Nerve Retina Lens Cornea Iris The Cornea is the bulge on the forward surface of the eye. The Iris is a coloured area with a hole in the centre called the pupil. Muscle tissue in the iris allows it to open and close the pupil to regulate the amount of light that gets inside the eyeball. The Lens is just behind the iris. The Retina is the light-sensitive layer that lines the inside of the eyeball. The Optic Nerve transmits signals from the retina to the brain which analyses them.

The cornea and the lens work together to focus images on the retina. Focal length mm The focal length that produces the image of a relaxed human eye is approximately 2 cm. This means that most objects relative to the eye are a very large distance away (at optical infinity). Therefore, the light rays coming from most objects can be considered to be parallel and will form an image at the Focus on the retina.

If the object is close to the eye, the light rays cannot be considered to be parallel. If the focal length remained the same, the image would focus behind the retina. Notice that the image on the retina is inverted. The brain inverts it again so that we see things correctly.

Fortunately, muscles around the lens can change its shape, thereby, changing its focal length. This causes the image to focus once again on the retina. This process is called accommodation. A young human eye can accommodate rays coming from objects that are as close as 7 cm from the eye. This is called the “Near Point”. However, this “Near Point” accommodation declines with age.

Light rays coming from distant objects are most easily seen because the eye does not have to accommodate in order to focus the rays onto the retina. All optical instruments are designed so that the eye does not have to accommodate in order to focus the rays onto the retina. This means that the light rays entering the eye are parallel (as if they were coming from a distant object).

Astronomical Telescope This is incorrect because the eye would have to accommodate the non-parallel rays refracting through the Ocular lens. Depending on how close the final image is, this may not be possible.

Astronomical Telescope If the Ocular lens is moved so that the image formed by the Objective……

Astronomical Telescope If the Ocular lens is moved so that the image formed by the Objective is on the Ocular’s Focus, then the rays refracted by the Ocular will be parallel. The eye would not have to accommodate them in order to get a clear image on the retina.

Astronomical Telescope Recall, in order to produce the LARGEST image POSSIBLE with a converging lens, the object (or image from previous lens) must be placed AT the FOCUS. The image’s characteristics are larger, inverted, virtual, & far away.

Terrestrial Telescope Terrestrial telescopes are very similar to the Astronomical Telescope. The first image is found the same way.

Terrestrial Telescope An extra erector lens is arranged so that the first image is at 2F of the Rectifying lens. This produces a second erect image at 2F of the Rectifying lens.

Terrestrial Telescope The Ocular Lens is moved so that the Rectifiers lens’ image is……

Terrestrial Telescope The Ocular lens is moved so that the Rectifiers Lens’ image is placed on the Ocular’s Focus. The Ocular’s refracted rays will, therefore, be parallel and the eye does not have to accommodate them in order to get a clear image on the retina.

Terrestrial Telescope The final image is where the rays refracted from the Ocular lens appear to come from. Only now it is larger, erect, virtual and far away (at optical infinity).

Terrestrial Telescope (Binoculars) Erector lens are actually not often used. Porro prisms are another way to rectify the image.

Terrestrial Telescope (Binoculars) Recall when a periscope faces backward, the image is inverted.

Terrestrial Telescope (Binoculars) Porro prisms work like a backward-looking periscope.

Terrestrial Telescope (Binoculars) The first Porro prism inverts the image top to bottom while the second prism inverts the image left to right.

Terrestrial Telescope (Binoculars) Binoculars are almost identical to the Terrestrial telescopes. The Objective lens image is found as usual.

The difference is that Porro prisms are used to rectify the image. The first prism inverts the image top to bottom while the second prism inverts the image left to right. Terrestrial Telescope (Binoculars)

Porro prisms do not change the location of the image; they just rectify it. The Ocular is placed so that the image…… Terrestrial Telescope (Binoculars)

Porro prisms do not change the location of the image; they just rectify it. The Ocular is placed so that the image is at its Focus. The refracted rays are, therefore, parallel so the eye does not have to accommodate. Porro prisms shorten the overall length of the binoculars. Terrestrial Telescope (Binoculars)

The final image is where the rays refracted from the Ocular lens appear to come from. It is larger, erect, virtual, & far away (at optical infinity).

Compound Microscope The simplest Compound Microscope also consists of only two lens, an Objective and an Ocular lens.

Compound Microscope The objects of Compound Microscopes are small and must be close to the Objective lens. The objects must be beyond the Focus in order to produce a real image.

Compound Microscope The Objective lens of Compound Microscopes must, therefore, have short focal lengths. This makes it possible to get closer to the object.

Compound Microscope The first image formed by the Objective lens is found as usual.

Compound Microscope An incident ray parallel to the principal axis refracts……

Compound Microscope An incident ray parallel to the principal axis refracts through the Focus of the Objective lens.

Compound Microscope An incident ray passing through the Focus of the Objective lens refracts……

Compound Microscope An incident ray passing through the Focus of the Objective lens refracts parallel to the principal axis.

Compound Microscope An incident ray passing through the Optical Centre of the Objective lens……

Compound Microscope An incident ray passing through the Optical Centre of the Objective lens does not refract and passes straight through.

Compound Microscope The first image of the Objective lens is where the refracted rays meet.

Compound Microscope The real image formed by the Objective lens acts like an object for the Ocular lens. The Ocular is placed so that the image……

Compound Microscope The real image formed by the Objective lens acts like an object for the Ocular lens. The Ocular is placed so that the image is at the Ocular’s Focus.

Compound Microscope An incident ray parallel to the principal axis refracts……

Compound Microscope An incident ray parallel to the principal axis refracts through the Focus of the Ocular lens.

Compound Microscope An incident ray passing through the Optical Centre of the Objective lens……

Compound Microscope An incident ray passing through the Optical Centre of the Objective lens does not refract and passes straight through.

Compound Microscope The Ocular is placed so that the Objective’s image is at the Ocular’s Focus. Therefore, refracted rays are parallel and the eye does not have to accommodate.

Compound Microscope The final image is where the rays refracted from the Ocular lens appear to come from. It is larger, inverted, virtual and far away (at optical infinity).

Galilean Telescope Galilean telescopes are a little tricky to understand. As usual for a telescope, an image is formed on the focal plane of the Objective lens.

Galilean Telescope A diverging lens is placed so that its secondary Focus……

Galilean Telescope A diverging lens is placed so that its secondary Focus is on the Objective’s image.

Galilean Telescope One of the incident rays heading toward the image will be parallel to the principal axis and will refract.

Galilean Telescope One of the incident rays heading toward the image will be parallel to the principal axis and will refract as if it had passed through the principal Focus.

Galilean Telescope Another of the incident rays heading toward the image will pass through the Optical Centre and will……

Galilean Telescope Another of the incident rays heading toward the image will pass through the Optical Centre and will not refract but pass undeviated (straight) through.

Galilean Telescope Notice that the refracted rays are again parallel and the eye does not have to accommodate.

Galilean Telescope The final image is where the rays refracted from the Ocular lens appear to come from. It is larger, erect, virtual, and far away (at optical infinity).

Optical Instrument Applet The Applet at allows one to create many different types of Optical Instruments containing converging and diverging lens and mirrors. It is an excellent way to review concepts. You can even add an eye and show the retinal image.