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Chapter 5: Lenses Please remember to photocopy 4 pages onto one sheet by going A3âA4 and using back to back on the photocopier
Two types of spherical lens: convex (which is also called âconvergingâ because it causes rays which are arrive parallel to the principle axis to converge) and concave (caves in as you look at it â also called âdivergingâ).
Convex (converging) lenses â ray diagrams You should be able to draw a ray diagram showing how an image is formed by a convex lens when the object is placed (i) outside the focus â resulting in a real image (ii) inside the focus â resulting in a virtual image
Three Rules From top of object to lens (parallel to principle axis) and after passing through the lens then passes through the focal point on the other side. From top of object through focal point and after passing through the lens continues on the other side parallel to the principle axis. Centre of Curvature: From top of object to centre of curvature and continues straight through.
For each of the following label the focal point , the object and the image. Put arrows on all rays, and state whether the image is real or virtual, upright or inverted, magnified or diminished
Object outside f Object inside f
Notice that when the object is inside the focal point the light rays never intersect, but from the viewerâs perspective they appear to do so behind the mirror (the viewer is to the right of the lens in the diagrams above).
Note A real image is always on the other side of the lens (to the object) and is inverted. A virtual image is always on the same side of the lens is upright.
Concave (diverging) lenses â ray diagrams Here only one diagram is needed; the image is always diminished, upright and virtual.
Two Rules (i) From top of object to the lens parallel to principle axis and up as if coming from the focal point. (ii) From top of object to the lens as if passing through centre of curvature.
Notice that in this situation (similar to the convex mirror when the object is inside the focus) light rays never intersect, but from the viewerâs perspective they appear to do so at the same side of the lens as the mirror. The image is therefore always virtual , regardless of where the object is placed.
Maths Problems
Relationship between focal length (f), object distance (u) and image distance (v)
Convention: For a convex lens f is positive For a concave lens f is negative
For a real image v is positive For a virtual image v is negative
The last two lines are what is referred to as the âReal is Positiveâ convention (RiP).
Remember that for a convex lens the image is only virtual if the object is inside the focus. For a concave lens the image is always virtual.
u is always positive for both types of lens
Magnification
If you are told that v is virtual, or if it is obvious from the question (because the lens is diverging or because the object is inside the focal length if the lens is converging) then you should make the value for v negative at the beginning of the question.
Note: If you are told that v is virtual, or if it is obvious from the question (because the lens is concave, or because the object is inside the focal length if the lens is convex) then you should make the value for v negative.
f u v
Defects of Vision; short and long-sightedness
Short Sight A Short-sighted person can see nearby objects clearly but cannot bring distant objects into focus.
Long Sight A Long-Sighted person can see distant objects clearly but cannot bring nearby objects into focus.
Leaving Cert Physics syllabus: Lenses
Content Depth of Treatment Activities STS
Lenses Images formed by single thin lenses. Knowledge that 1/f = 1/v + 1/u
Simple exercises on lenses by ray tracing or use of formula.
Use of lenses
m = v/u
Power of lens: P = 1/f
Two lenses in contact: P = P 1 + P 2
The eye: Optical structure, short sight, long sight, and corrections.
Spectacles
MEASUREMENT OF THE FOCAL LENGTH OF A CONVEX LENS
APPARATUS
Converging lens, screen, lamp-box with crosswire, metre stick, retort stand.
DIAGRAM
PROCEDURE
- Place the ray-box well outside the approximate focal length.
- Move the screen until a clear inverted image of the crosswire is obtained.
- Measure the distance u from the crosswire to the lens, using the metre stick.
- Measure the distance v from the screen to the lens.
- Repeat this procedure for different values of u.
- Calculate the focal length of the lens each time using the formula
f u v
= + and get an average.
- Plot a graph of 1/u against 1/v and use the intercepts to get two values for f. Then get the average of these two.
RESULTS Object distance u 1/u
Image distance v 1/v
Focal Length f
CONCLUSION Using the graph we got an average value for the focal length of the lens of 25.6 cm. From the table of data we got an average value of 24.4 cm, which was close to the value we got from the graph, suggesting that both readings are reasonably accurate.
SOURCES OF ERROR / PRECAUTIONS
- Determining when the image was in sharpest focus; repeat each time and get an average.
- Parallax error associated with measuring u and v; ensure your line of sight is at right angles to the metre stick.
- Take all measurements from the centre of the lens.
NOTES How to find an approximate value for the focal length.
- Focus the image of a distant object onto a screen.
- Measure the distance between the lens and the screen.
- This corresponds to an approximate value for the focal length of the lens.
Using the graph to calculate the focal length It is also possible to draw a graph, on graph paper, of 1/v (y-axis) against 1/u. The equation of the line can be compared to the standard form of linear equation, y = mx + c. In this case it is: 1/v = -1/u + 1/f. This cuts (intercepts) the y-axis (1/v axis) when x (1/u) is zero i.e. 1/v = 0 + 1/f. Similarly the line intercepts the 1/u axis when 1/v is zero, giving us 1/u = 1/f. From your graph get the average of the two intercepts, find the reciprocal to get the value of f.
seemed to be upright rather than inverted. On the fifth day, he was able to walk around his house fairly normally but he found that if he looked at objects very carefully, they again seemed to be inverted. On the whole, Stratton reported that his environment never really felt normal especially his body parts, although it was difficult to describe exactly how he felt. He also found that after removing the reversing lenses, it took several hours for his vision to return to normal.
Three sons bought a farm and named it âThe Focal Pointâ. When their father asked why they chose that name, they replied, âItâs the place where the sons raise meatâ.
