Optional Unit VI: Optics

Optional Unit VI: Optics
B. Lenses

Key Concepts

Lenses have curved surfaces, or a very large number of flat surfaces located at slightly different angles. (i.e., Fresnel lens)

Converging lenses (positive lenses) are thicker at the centre than at the edges.

Diverging lenses (negative lenses) are thicker at the edges than at the centre.

(Only thin, single lenses are dealt with in Physics 20. Note as well that the terms concave and convex, as applied to lenses, can be misleading. A meniscus lens has both a concave and a convex surface, but the thickness at the centre compared with the edges determines if it behaves as a conver 12212k103m ging or a diverging lens.)

The optical centre of the lens is located at its geometric centre.

The principal axis is a construction line drawn perpendicular to the lens, through the optical centre.

Rays parallel to the principal axis will converge when passing through a converging lens, and diverge when passing through a diverging lens.

The principal focus (F) is a point on the principal axis where light comes to a focus (for a converging lens) or appears to be diverging from (for a diverging lens). Two foci exist, equidistant on either side of the lens, since light behaves the same way when travelling in either direction (Principle of Reversibility). The two foci, F and F' are called the primary principal focus and the secondary principal focus, respectively. F, sometimes also referred to as the primary focal point, is shown on the right side of a converging lens, and on the left side of a diverging lens, while F', the secondary focal point is shown on the opposite side of each respective lens.)

Ray diagrams are used to show rays passing through a lens.

Ray diagrams can be useful in determining the characteristics of an image formed by a lens.

By convention, incident rays are shown travelling from left to right on ray diagrams. A dotted line is usually drawn through the lens at the optical centre, perpendicular to the principal axis.

Ray diagrams should always be drawn and labelled neatly, accurately, and to some appropriate scale.

The focal length is the distance between the principal focus and the optical centre of the lens.

The focal plane is an imaginary plane perpendicular to the principal axis at the focal point. Parallel rays will converge through a converging lens somewhere on the focal plane.

Incident light rays are refracted twice by a lens; once at each boundary. Partial reflection may also occur. (In optical systems, partial reflection is undesirable. It can be minimized by using optical lens coatings. Coated lenses provide superior image quality.)

To simplify matters on ray diagrams, incident rays can be shown to refract at the construction line passing through the optical centre of the lens. For a thin lens this leads to a reasonably close approximation because the lateral displacement is quite small.

Light rays that have travelled over a large distance are effectively parallel.

Lenses can form either real or virtual images.

The rules for drawing ray diagrams for converging and diverging lenses can be used to determine the characteristics of an image formed by a lens.

Lens equations can be used to determine the characteristics of an image. (Refer to page 111 for lens equations and sign conventions.)

A diverging lens always forms an erect, virtual image which is diminished in size. It is located closer to the lens than the object, between the principal focal point and the lens.

To correct for spherical aberration in lenses, achromatic lenses can be used. (Spherical aberration in lenses can be corrected by using aspheric lenses, or by using thin lens combinations which cancel out aberrations. Achromatic lenses, designed to correct for chromatic aberration at some wavelengths, can also help to reduce spherical aberration.)

Lens defects are called aberrations. They hinder the quality of the image formed in an optical system.

Lenses are used in many different kinds of practical applications. (Several should be studied.)

An optical system may use a combination of mirrors, lenses, prisms, and other kinds of optical devices.

An image formed by one component in an optical system can serve as an object for a different component.

The image characteristics formed by converging lenses depend on the location of the object. This table summarizes the characteristics of images found in a converging mirror based onthe location of the object.

Image Characteristics

(These characteristics should be developed experimentally, and verified with the use of ray diagrams and equations. Rote memorization should be discouraged and avoided.)

Rules for Drawing Ray Diagrams for Converging and Diverging Lenses

(Parenthetical remarks refer specifically to diverging lenses)

1. An incident ray that is parallel to the principal axis is refracted such that it passes through (or appears to have originated from) the principal focus (F).
2. An incident ray passing through (or heading toward) the secondary principal focus (F') is refracted such that it travels parallel to the principal axis.
3. An incident ray passing through the optical centre of the lens continues to travel in a straight line.

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: converging (positive) lens, diverging (negative) lens, optical centre, principal axis, principal focus, focal length, focal plane, achromatic lens, virtual object.
2. Distinguish between a converging (positive) lens and a diverging (negative) lens.
3. Draw diagrams of converging and diverging lenses, showing the principal axis and important points on the principal axis for each type of lens.
4. Draw neat, properly labelled, accurate, scaled ray diagrams for single thin lenses.
5. Apply the rules for drawing ray diagrams for converging and diverging lenses (parallel-ray method) to draw an object on the principal axis and locate the position and other characteristics of its image.
6. Use a ray diagram to interpret the characteristics of an image formed by a lens.
7. Demonstrate an understanding of the importance and use of a procedure of verification.
8. Recognize that, even though light rays are refracted at both surfaces by a lens, for thin lenses the incident rays can be shown refracting at the construction line passing through the optical centre of the lens.
9. Explain why light rays travelling over a long distance are effectively parallel when they reach a lens (or other type of optical system).
10. Apply lens equations, in conjunction with ray diagrams and other methods, to solve problems in optics dealing with lenses.
11. Explain one method that can be used to correct for spherical aberration in lenses.
12. Distinguish between a real object and a virtual object.
13. Identify various useful applications of lenses, and show their importance to society.

Teaching Suggestions, Activities and Demonstrations

1. Perform an activity to investigate image formation in converging and diverging lenses.
2. Place a light source, a converging lens, and a screen on a stand. Determine the image position at various different distances between the object and the lens. Find the focal length and the lens power. Determine the magnification for specific object positions. Repeat with several different positive lenses. Draw ray diagrams illustrating each specific case. State the image characteristics for all of the possible cases. For an added challenge, repeat using two different lenses placed together.
3. Place a converging and a diverging lens on an optical bench. Look through the lens combination from both directions at distant objects. Adjust the separation of the lenses.
4. The arrangement described in #3 above was used to develop the first optical telescopes. Background historical information on the development of the telescope could be researched independently by students.
5. Compare Galilean and Keplerian telescopes in terms of image characteristics. Using ray diagrams and data collected through experimentation, show how the image is formed in each of the telescopes.
6. Various ray box demonstrations and activities are useful to incorporate into this section.
7. Use computers as analytical tools to solve problems, perform simulations, and explore new environments in micro worlds.
8. A useful model which simulates the refraction of sunlight through the atmosphere involves preparing a solution in a beaker which contains about 900 mL of water, 5 g of sodium thiosulphate and 5 mL of concentrated hydrochloric acid. (Always add the acid to water. Never add water to the acid. The solution is fairly safe when diluted, but the concentrated acid is very corrosive.)

A colloidal solution of sulphur forms. Shine a spotlight through the container. Scattered blue light will be evident at right angles to the beam. Use a white screen to examine different regions of the beam. The colours will appear white, yellow, and red. Regions that are blackened completely may also be evident.

This demonstration is useful for explaining sunsets and the Tyndall Effect. (Save the solution. Pour it into a round-bottomed Florence flask to simulate refraction in lenses.)