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If each side of a lens has a spherical shape with a radius of curvature (R), the lens is called a spherical lens. Notice that the curvature of the two surfaces can be different. In fact one side can be convex and the other concave. |
| Spherical Lenses | |
|---|---|
| Optical Bench | Light Source |
| Lens (concave) | Lens (convex) |
| Concave Lens with holder (2) | |
Purpose: to examine the geometry involved in the forming of real images in spherical lenses.
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If each side of a lens has a spherical shape with a radius of curvature (R), the lens is called a spherical lens. Notice that the curvature of the two surfaces can be different. In fact one side can be convex and the other concave. |
The following figure shows a convex lens. A convex lens is called a converging lens because rays parallel to the principal axis converge at the focal point.
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The following figure illustrates concave lens is called a diverging lens because rays parallel to the principal axis appear to diverge from the focal point.
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Study the following definitions which are illustrated in preceding figures.
Radius of Curvature (R) -- The radius of curvature defining the shape of the lens for either the concave and convex surface.
Principal Axis (PA) -- The principal axis is the line passing through the center of the lens and is perpendicular to the surface. It is also the axis of symmetry.
Focal Point and Focal Length -- A ray of light, which is parallel to the principal axis (PA) and incident on a convex lens will be refracted through point F which is known as the focal point. The distance, OF , is known as the focal length of the concave lens.
A ray of light, which is parallel to the principal axis (PA) and incident on a concave lens will be refracted away from the axis and appear to diverge from point F, which is the focal point. The distance OF is the focal length.
Virtual and Real Focus -- In the case of a convex lens, the rays of light converge and pass through F. This point is known as a real focus. In the case of the diverging lens the parallel rays of light appear to diverge from F and it is known as a virtual focus.
Object Distance (do) -- The distance from the center of the lens to the position of the object is known as the object distance.
Image Distance (di) -- The distance from the center of the lens to the position of the image is known as the image distance.
Magnification (M) -- Magnification is defined as the size of the image (h') divided by the size of the object (h).
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Real Image -- At a real image, the light actually passes through the point to reproduce the object.
Virtual Image -- At a virtual image, the light appears to emerge from the position of the image.
| 1. | If the ray goes parallel to the axis, then it will be refracted through the focal point. |
| 2. | If the ray goes through the focal point, it is refracted parallel to the optical axis. |
| 3. | If the ray enters along the radius of curvature, then it is refracted along the same line. |
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| Figure 4 |
| 1. | If the ray goes parallel to the axis, then it will be refracted as to appear that it came from the focal point. |
| 2. | If the ray would go through the focal point (if it kept going), it is refracted parallel to the optical axis. |
| 3. | If the ray enters along the radius of curvature, then it is refracted back along the same line. |
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| Figure 5 |
We can obtain an equation which relates the focal length (f), the object distance (do) and the image distance (di).
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However, in using this equation one must pay attention to the sign (positive or negative) of the various quantities involved.
| 1. | Object distances (do) are positive if the object is real, negative if the object is virtual. |
| 2. | Image distances (di) are positive if the image is real, negative if the image is virtual. |
| 3. | The focal length is positive for a converging lens; it is negative for diverging lens. |
| 1. | Place a blank sheet of white paper on the table. |
| 2. | Place the light box and the concave lens on the sheet of paper. |
| 3. | Adjust the number of beams from the light box to 4. |
| 4. | Arrange the light box and the concave mirror so that the beams are parallel to the principle optical axis of the mirror. |
| 5. | With a pencil, plot a point at each end of all four original beams and their refractions. |
| 6. | Draw in all eight beams and the lens. |
| 7. | Extend the refractions in order to locate the virtual focal point. |
| 8. | Then measure the focal length |
| 1. | Place a blank sheet of white paper on the table. |
| 2. | Place the light box and the convex lens on the sheet of paper. |
| 3. | Adjust the number of beams from the light box to 4. |
| 4. | Arrange the light box and the convex mirror so that the beams are parallel to the principle optical axis of the lens. |
| 5. | With a pencil, plot a point at each end of all four original beams and their refractions. |
| 6. | Draw in all eight beams and the mirror. |
| 7. | Then measure the focal length. |
| 1. | Place the light box at the 0 mark and the screen at 110 cm. |
| 2. | Find 2 positions for the lens that will produce images on the screen. |
| 3. | Measure the object and image height. |
| 3. | Do all the calculations suggested in the data table. |
| 4. | Repeat the first four steps after moving the screen to the 100, and 90 cm positions. |
| 5. | Find the screen and lens position such that the object distance is equal to the image distance and the magnification is equal to 1. This could be easier if you get a tentative answer for the next step first. |
| 6. | Find the average focal length from the above 6 data points. |
| Screen Position cm |
Lens Position cm |
ho cm |
hi cm |
do cm |
di cm |
M hi/ho |
M di/do |
M %dif |
Focal Length cm |
| 110 | |||||||||
| 110 | |||||||||
| 100 | |||||||||
| 100 | |||||||||
| 90 | |||||||||
| 90 | |||||||||
| 3.0 | 3.0 | 1 | 1 | ||||||
| Average Focal Length | |||||||||
| 1. | How can we tell in Figure 4 that the image is real? |
| 2. | How can we tell in Figure 5 that the image is virtual? |
| 3. | What is the focal length in procedure A? |
| 4. | What is the focal length in procedure B? |
| 5. | Given a focal length (convex lens) of 10 cm, where would be image be if the object distance was 15 cm? What are the characteristics of the image? |
| 6. | Given a focal length (convex lens) of 10 cm, where would be image be if the object distance was 5.0 cm? What are the characteristics of the image? |