12.3 Telescopes and microscopes  (Page 2/2)

[link] shows that when an object is placed at a distance less than $f$ from the lens, the image formed is virtual, upright and is larger than the object. This set-up is a simple magnifier.

If you want to look at something very small, two lenses may work better than one. Microscopes and telescopes often use two lenses to make an image large enough to see.

A compound microscope uses two lenses to achieve high magnification ( [link] ). Both lenses are convex, or converging. Light from the object first passes through the objective lens . The lens that you look through is called the eyepiece . The focus of the system can be adjusted by changing the length of the tube between the lenses.

Drawing a Ray Diagram for a Two-Lens System

You already have all the tools to analyze a two-lens system. Just consider one lens at a time.

1. Use ray tracing or the lens equation to find the image for the first lens.
2. Use the image of the first lens as the object of the second lens.
3. To find the magnification, multiply: $m_{total}=m_1\times m_2\times m_3\times ...$

Summary

1. A lens is any transparent material that is shaped in such a way that it will converge parallel incident rays to a point or diverge incident rays from a point.
2. Converging lenses are thicker in the middle than on the edge and will bend incoming light rays towards the principal axis.
3. Diverging lenses are thinner in the middle than on the edge and will bend incoming light rays away from the principal axis.
4. The principal axis of a lens is the horizontal line through the centre of the lens.
5. The centre of the lens is called the optical centre.
6. The focus or focal point is a point on the principal axis where parallel rays converge through or diverge from.
7. The focal length is the distance between the focus and the optical centre.
8. Ray diagrams are used to determine the position and height of an image formed by a lens. The properties of images formed by converging and diverging lenses are summarised in [link] .
9. The human eye consists of a lens system that focuses images on the retina where the optic nerve transfers the messages to the brain.
10. Defects of vision include short-sightedness, long-sightedness and astigmatism.
11. Massive astronomical bodies, such as galaxies, act as gravitational lenses that can change the apparent positions of the images of stars.
12. Microscopes and telescopes use systems of lenses to create magnified images of very small or very distant objects.

Exercises

1. Select the correct answer from the options given:
   1. A $............$ ( convex/concave ) lens is thicker in the center than on the edges.
   2. When used individually, a ( diverging/converging ) lens usually forms real images.
   3. When formed by a single lens, a $............$ ( real/virtual ) image is always inverted.
   4. When formed by a single lens, a $............$ ( real/virtual ) image is always upright.
   5. Virtual images formed by converging lenses are $............$ ( bigger/the same size/smaller ) compared to the object.
   6. A $............$ ( real/virtual ) image can be projected onto a screen.
   7. A $............$ ( real/virtual ) image is said to be "trapped" in the lens.
   8. A ray that starts from the top of an object and runs parallel to the axis of the lens, would then pass through the $............$ ( principal focus of the lens/center of the lens/secondary focus of the lens ).
   9. A ray that starts from the top of an object and passes through the $............$ ( principal focus of the lens/center of the lens/secondary focus of the lens ) would leave the lens running parallel to its axis.
   10. For a converging lens, its $............$ ( principal focus/center/secondary focus ) is located on the same side of the lens as the object.
   11. After passing through a lens, rays of light traveling parallel to a lens' axis are refracted to the lens' $............$ ( principal focus/center/secondary focus ).
   12. Real images are formed by $............$ ( converging/parallel/diverging ) rays of light that have passed through a lens.
   13. Virtual images are formed by $............$ ( converging/parallel/diverging ) rays of light that have passed through a lens.
   14. Images which are closer to the lens than the object are $............$ ( bigger/the same size/smaller ) than the object.
   15. $............$ ( Real/Virtual ) images are located on the same side of the lens as the object - that is, by looking in one direction, the observer can see both the image and the object.
   16. $............$ ( Real/Virtual ) images are located on the opposite side of the lens as the object.
   17. When an object is located greater than two focal lengths in front of a converging lens, the image it produces will be $............$ ( real and enlarged/virtual and enlarged/real and reduced/virtual and reduced ).
2. An object 1 cm high is placed 1,8 cm in front of a converging lens with a focal length of 0,5 cm. Draw a ray diagram to show where the image is formed. Is the final image real or virtual?
3. An object 1 cm high is placed 2,10 cm in front of a diverging lens with a focal length of 1,5 cm. Draw a ray diagram to show where the image is formed. Is the final image real or virtual?
4. An object 1 cm high is placed 0,5 cm in front of a converging lens with a focal length of 0,5 cm. Draw a ray diagram to show where the image is formed. Is the final image real or virtual?
5. An object is at right angles to the principal axis of a convex lens. The object is 2 cm high and is 5 cm from the centre of the lens, which has a focal length of 10 cm. Find the distance of the image from the centre of the lens, and its height. Is it real or virtual?
6. A convex lens of focal length 15 cm produces a real image of height 4 cm at 45 cm from the centre of the lens. Find the distance of the object from the lens and its height.
7. An object is 20 cm from a concave lens. The virtual image formed is three times smaller than the object. Find the focal length of the lens.
8. A convex lens produces a virtual image which is four times larger than the object. The image is 15 cm from the lens. What is the focal length of the lens?
9. A convex lens is used to project an image of a light source onto a screen. The screen is 30 cm from the light source, and the image is twice the size of the object. What focal length is required, and how far from the source must it be placed?
10. An object 6 cm high is place 20 cm from a converging lens of focal length 8 cm. Find by scale drawing the position, size and nature of the image produced. (Advanced: check your answer by calculation).
11. An object is placed in front of a converging lens of focal length 12 cm. By scale diagram, find the nature, position and magnification of the image when the object distance is
    1. 16 cm
    2. 8 cm
12. A concave lens produces an image three times smaller than the object. If the object is 18 cm away from the lens, determine the focal length of the lens by means of a scale diagram. (Advanced: check your answer by calculation).
13. You have seen how the human eye works, how telescopes work and how microscopes work. Using what you have learnt, describe how you think a camera works.
14. Describe 3 common defects of vision and discuss the various methods that are used to correct them.