Converging Lenses Converging lenses change the direction of light through refraction so that the light rays all meet (converge) on a single focal point. Lens Axis Principal Focus Axial light rays Principal Axis Axial rays passing through a lens and converging on the principal focus

Converging Lenses The focal length is found by focussing a distant object on a screen or detector through the lens. The focal length is the distance between the centre of the lens and the image. Lens Axis Principal Focus Axial light rays Principal Axis Axial rays passing through a lens and converging on the principal focus

A plane perpendicular to the principal axis Rays that are parallel to the principal axis are called axial rays. They will converge on the principal focus. Non axial rays do not focus here, but somewhere on the focal plane. Focal Plane A plane perpendicular to the principal axis Lens Axis Principal Focus Axial light rays Principal Axis Axial rays passing through a lens and converging on the principal focus

Parallel non axial rays Focal Plane Principal Axis

Drawing Ray Diagrams for images Draw an axial ray from the top of the object to the lens axis. Connect this through the principal focus. Draw a second ray from the top of the object through the centre of the lens (where the lens axis and the principal axis cross) that doesn’t get refracted at all. Principal Focus Principal Axis Make sure the object is further away from the lens than the focal plane!

Real Images A real image is the image formed when light rays from a point on an object are made to pass through another point in space. The light rays are actually there and so can be seen on a screen

Virtual Images A virtual image is formed when light rays from an object appear to come from another point in space where the object isn’t. The light rays aren’t really there and cannot be captured on a screen.

Principal Focus Principal Axis

Lens based telescopes A converging lenses are used in a refracting telescope to focus the image. They are generally made up of two converging lenses: The first one, called the objective lens focuses the light from distant stars and creates a real image. The second one, called the eye lens, acts as a magnifying glass for you to view the real image. As star light reaches us from a very large distance away, we approximate the rays of light we receive to be completely parallel.

The Diagram  Objective lens Eye lens Real image formed Magnified virtual image at infinity

Step by step how to a ray diagram for an astronomical telescope in normal adjustment Draw a straight, non axial ray that passes through the centre of the objective lens and ends at the eye lens axis. Draw two parallel non axial rays either side of the first one, ending at the objective lens. Join these two lines to the point where the first ray meets the focal plane and extend them to the eye lens. A real image is formed at the focal point. Draw a straight dotted line through this point and out through the centre of the eye lens (this is a construction line and not a ray of light). Draw your rays of light leaving the eye lens parallel to this line... And your done 

Angular Magnification The magnification, M, of a telescope can be found by looking at the angles or the focal length. The angular magnification is the angle subtended by the image when viewed through a lens divided by the angle subtended by the object at an unaided eye.

Angular Magnification Using the focal length, the magnification, M, of an astronomical telescope in normal adjustment is found by: where, fo is the focal length of the objective lens and fe is the focal length of the eye lens

Another way of looking at it... If you know the size of the object you are viewing, and the distance to it, you can calculate the angle subtended by the image: where s is the size of the object and r is the distance.

The problem with refracting telescopes Chromatic aberration splits colours like refracting them through a prism, so different colours focus at different points on the principal axis. Bubbles and impurities in the glass can cause scattering, distorting small objects so the cannot be seen. Creating large lenses without impurities is difficult and expensive, not to mention how heavy they are! For large magnification, the lens needs a long focal length, therefore they can need large, expensive buildings to house them.

40 ft telescope. Note the guy on the left...

Resolving power Resolving power is a measure of how much detail you can see using a telescope. You can have a very high magnification, but if your resolving power is low, your image will always be blurry  Resolution is limited by diffraction through the aperture of your telescope, or the lens to you and me.

Changing the diameter of the lens changes the resolving power of the lens The larger the diameter of the lens, the better the resolving power. This means you can resolve objects that are closer together (i.e. Have small angles between them).

Resolving power

In terms of the light intensity...

Rayleigh Criterion Two light sources can just be distinguished (resolved) if the centre of the Airy Disc is at least as far away as the first minimum for the other source. Or in other words, when the central maxima of the Airy Discs don’t overlap at all. where θ is the minimum angle that can be resolved in radians, λ is the wavelength in metres and D is the diameter of the aperture (in this case the lens, but also the mirror in reflecting telescopes).

Have a go at the question. Here is the stuff from the Data Sheet