Lenses

There are 8 planets in our Solar System. In order of distance from the Sun:

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

Our Solar System is in the Milky Way Galaxy.

Objects that orbit planets are called satellites. The Moon is a natural satellite of Earth. The International Space Station (ISS) is an artificial satellite orbiting the Earth.

Observations of the moons of Jupiter by Galileo Galilei proved that not all celestial objects orbit the Earth, disproving the geocentric model at the time and replacing it with the heliocentric model (with the Sun at the centre of the Solar system), challenging the Catholic Church.

Everything we know about our Solar System and beyond came from the careful study of light, either via lenses or mirrors. Therefore, understanding how we can capture light and how lenses work is of fundamental importance to this area of science.

Refraction is the change in the direction of light as it passes from one medium into another. When light travels into a medium with a higher refractive index, such as from air into glass, its direction changes. The light ray bends towards the normal, as the speed of light decreases in this more optically dense medium.

Lenses use refraction to bring light rays to a focus at a single point.

Convex or converging lenses bring rays of light to a focus at the principal focus/focal point. Used in cameras, projectors, the human eye, magnifying glasses and telescopes.

When drawing ray diagrams for lenses, we use the rules below for convex lenses:

A concave or diverging lens makes parallel rays of light diverge. The point from which the rays appear to come is the principal focus/focal point. Used to correct short-sightedness (myopia) as people can’t see things that are far away. The lens in the eye is too strong, bringing rays of light to a focus before the retina. A diverging lens placed in front of the eye causes the light rays from the distant object to spread out before they reach the eye, enabling the distant object to be seen more clearly.

You need to understand how lenses work to understand how the two main astronomical telescopes were designed and are used. Refracting telescopes use two convex lenses, and reflecting telescopes that use a large concave primary mirror work. You also need to know how to sketch diagrams of these two telescopes.

Normal Adjustment Refracting Telescopes

The first lens (the objective) collects the light from a distant object and brings it to a focus in its focal plane. The second lens (the eyepiece) uses this light to form a magnified image at infinity. This is achieved by placing the lens so that its focal plane coincides with the focal plane of the objective. The sum of the focal lengths is equal to the distance between the objective lens and the eyepiece lens.

-> Tips for drawing a Normal Adjustment Refracting Telescope

1. Start by drawing a principal axis, then drawing and labelling the lenses. 
2. Mark and label the common principal foci, .
3. Draw an off-axial ray through the centre of the objective to the eyepiece and draw on the intermediate image formed. 
4. Draw a construction line from the end of the intermediate image through the centre of the eyepiece as a reference for later.
5. Draw two more non-axial rays from the object through the objective lens to the eyepiece, crossing at the end of the intermediate image.
6. Draw three rays from the eyepiece parallel to the construction line.
7. Add dotted lines continuing these back to show the magnified Image formed at infinity.

A problem with these telescopes is chromatic aberration. This occurs as light changes direction when entering the lens. Since all colours travel at different speeds, we end up with different colours of light being brought to a focus at different points, resulting in an image with coloured edges.

Lens power

Formula:

A more powerful lens can focus light closer to the lens.

Measured in dioptres, D.

Magnification refers to the process of making an image appear larger than the actual object.

Formula:

To calculate magnifying power / angular magnification of a telescope, we can use the equations below:

Formula:

We apply these equations when designing and using astronomical telescopes.

The largest (and therefore best) telescopes are reflectors.

Parallel rays of light enter the telescope from a distant object. The large primary parabolic concave mirror reflects the light onto the secondary convex mirror, which reflects the light out through a hole in the primary concave parabolic mirror.

The primary mirror is parabolic in shape to avoid spherical aberration.

Spherical aberration is caused as off axial rays are brought to a focus closer to the mirror.

Spherical aberration occurs in both reflecting and refracting telescopes, but can only be avoided in reflecting telescopes due to their parabolic shape, as mentioned previously.