THIN LENSES.

SPECIFIC OBJECTIVES.

1. Distinguish between converging and diverging lenses.
2. Define the principal axis, principal focus, focal length and center of curvature.
3. Describe the characteristics of images formed by convex and concave lenses.
4. Determine the focal length of convex lense.
5. Describe the operation of devices that use lenses.
6. Solve numerical problems using lense formula.

                                                Lenses.

• There are two types of lenses.

1. Convex or converging lenses.

• These are lenses that are thicker at the center than at the edges.
• They converge the rays of light at a point.
• They have a real or positive focal length.
• They form both real and virtual images.

1. Concave or diverging lenses.

• These are lenses that are thicker at the edges than at the center.
• They diverge the rays of light.
• They have negative focal length.
• They form virtual images only.

                                    Features of lenses.

1. The center of curvature- is the center of the sphere from which the lense was cut.
2. Radius of curvature- is the distance from the circumference of the sphere of which the lense forms a part to the optical center of the lense.
3. Optical center O- is the center of the lense or is the point on the principal axis midway between the lense surface.
4. Principal axis- is the line which passes through the middle of the lense joining the respective center of curvature.
5. Principal focus/focal point- is a point on the principal axis at which rays parallel and close to the principal axis converge after refraction(convex lense) or appear to meet after refraction by concave lense.
6. Focal plane- is a plane perpendicular to the principal axis and pass through the principal focus where rays that are not parallel to the principal axis meet after refraction by convex lense or appear to meet by concave lense.
7. Focal length- is the length between the principal focus and the optical center of a lense.

                                                Image.

• An image is formed whenever two or more rays meet or appear after refraction through the lense.
• There are two types of images;

1. Real image.

• Is an image that can be formed or focused on the screen.
• Is formed by real rays meeting after refraction.
• Is formed on the opposite side of a lense as the object.
• It is always inverted.
• It is represented by a complete line.

1. Virtual image.

• Opposite as the real image.
• Image is upright.
• Cannot be focused on the screen.

                                    Image construction by lenses.

• There are 3 rays used to locate an image formed by lenses.

1. A ray that is parallel to the principal axis and after refraction passes through the principal focus.
2. A ray passing through the principal focus emerge parallel to the principal axis after refraction.
3. A ray passing through the optical center of the cell passes undeviated.

Characteristics of images formed by lenses.

1. Object at infinity.

The image is;

• At F (the principal focus).
• Rea.l
• Inverted.
• Smaller than the object or diminished.
• This arrangement is used in the objective lense of a telescope.

1. Object beyond 2F.

The image is;

• Between F and 2F.
• Real.
• Inverted.
• Smaller than the object.
• The arrangement is used in the human eye and camera.

1. Object at 2F.

The image is;

• At 2F.
• Real.
• Inverted.
• Same as the object.
• The arrangement is used in copying camera and terrestrial telescope.

1. Object between F and 2F.

The image is;

• Beyond 2F.
• Real.
• Inverted.
• Bigger than the object.
• The arrangement is used in the objective lense of a microscope.

1. Object at F.

The image is;

• At infinity.
• Real.
• Inverted.
• The arrangement is used in sport lights and search lights.

1. Object between F and the lense.

The image is;

• Upright.
• Virtual.
• Bigger than the object.
• The arrangement is used in magnifying glasses and microscope eye piece.

                                                Concave lense.

• Forms virtual images at all positions of the object.

The images are;

• Formed on the same side of lenses as the object.
• Virtual.
• Upright.

                                    Power of a lense.

• Is the reciprocal of the focal length.

                        Power = 1/f

            SI units is diopter D

                                    Lense formula.

• Consider an object O at a distance U at a convex lense of focal length F. If an image I I formed on a screen which is a distance V from the lense, then the focal length of the lense is given by

            1/u + 1/v = 1/f.       This is the lense formula and is applied to both converging and diverging lenses.

• The numerical values of f, u and v are substituted in the formula with their appropriate sign.
• The convex lens has a real focal length since it has a real principal focus hence f is positive.

            1/u + 1/v = 1/f

• The concave lense has a negative focal length since the principal focus is formed by imaginery rays meeting hence f is negative.

            1/u + 1/v = -1/f

                                    Sign convection.

• Real is positive. All real distances and images are taken to be positive i.e. all measurement taken on the opposite side of the lense as object are positive.
• Virtual is negative. All virtual images and distances are taken as negative i.e. measurement taken on the same side of the lense as the object are negative.

                                    Magnification.

• Is the number of times an image is larger than the object.
• Is the ratio of image distance to object distance.

      M = v/u

• Is the ratio of image size to object size

        M = I/O

• From lens formula;

      1/u + 1/v = 1/f

      v/u + v/v = v/f         (multiply both sides by v)

      M + 1 = V/F

      M = V/F – 1

EXP: TO MEASURE THE FOCAL LENGTH OF A CONVEX LENSE.

Requirements.

1. Convex lense.
2. Lense holder.
3. Screen.
4. Meter rule.

Procedure.

1. Focus a distant object using the lense and the screen.
2. Measure the distance between the screen with a clear image and the lense screen.
3. Repeat the experiment for different objects and find the image.

Application or uses of lenses.

1. The eye.
2. Camera.
3. Microscope.
4. Telescope.
5. Prism binoculars.
6. Cinema projector.
7. Projection lanten.