# Lenses - General Physics - Lecture Notes, Study notes for Physics. Birla Institute of Technology and Science

## Physics

Description: This is the Lecture Notes of General Physics which includes Potential Difference and Capacitance, Charge of Coulomb, Unit of Potential Difference, Work, Charge and Voltage, Positive Charge, Symbol for Capacitance etc. Key important points are: Lenses, Types of Spherical Lens, Convex Lenses, Ray Diagrams, Centre of Curvature, Parallel to Principle Axis, Focal Length, Object Distance, Image Distance, Two Lenses in Contact
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Lenses

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Chapter 5: Lenses Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier

Two types of spherical lens: convex (which is also called ‘converging’ because it causes rays which are arrive parallel to the principle axis to converge) and concave (caves in as you look at it – also called ‘diverging’).

Convex (converging) lenses – 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 – resulting in a real image (ii) inside the focus – 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 viewer’s 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 – 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 viewer’s 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.

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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 ‘Real is Positive’ 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.

vuf 111 +=

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Power of a Lens* Power of a Lens = 1/focal length The unit of power is m-1. Convention The power of a converging (convex) lens is taken as positive (+) {because f is positive}. The power of a diverging (concave) lens is taken as negative (-) {because f is negative}.

Two Lenses in Contact

If two lenses of power P1 and P2 are placed in contact, the power P of the combination is given by Remember to use the correct sign notation. It follows from this that if two lenses of focal length f 1 and f2 are placed in contact, the focal length f of the combination is given by Remember to use the correct sign notation. Now look over problems 6 – 8, page 52, then try questions 1 – 10, page 53.

The Eye* Retina - light sensitive screen at the back of the eye, Optic Nerve – carries the information in electrical form to the brain Cornea – together with The Lens, form part of the focusing system. Iris – acts like a shutter to control the amount of light entering the eye

Power of Accommodation (page 54) The Power of Accommodation of the eye is its ability to focus a real image of an object on the retina, whether the object is near to or far away from your eye.

PTotal = P1 + P2

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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 = P1 + P2

The eye: Optical structure,

short sight, long sight, and corrections.

Spectacles

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MEASUREMENT OF THE FOCAL LENGTH OF A CONVEX LENS APPARATUS Converging lens, screen, lamp-box with crosswire, metre stick, retort stand. DIAGRAM PROCEDURE 1. Place the ray-box well outside the approximate focal length. 2. Move the screen until a clear inverted image of the crosswire is obtained. 3. Measure the distance u from the crosswire to the lens, using the metre stick. 4. Measure the distance v from the screen to the lens. 5. Repeat this procedure for different values of u.

6. Calculate the focal length of the lens each time using the formula vuf 111 += and get an average.

7. 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 1. Determining when the image was in sharpest focus; repeat each time and get an average. 2. Parallax error associated with measuring u and v; ensure your line of sight is at right angles to the metre stick. 3. Take all measurements from the centre of the lens. NOTES How to find an approximate value for the focal length. 1. Focus the image of a distant object onto a screen. 2. Measure the distance between the lens and the screen. 3. 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.

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Extra Credit Confusion with Mirrors and Lenses Whereas a concave mirror gives a real image (unless the object was inside the focus) this time it’s a convex lens which gives a real image (unless the object is inside the focus) and a concave lens always gives a virtual image. Secondly, whereas with mirrors a virtual image was always formed behind the mirror, with lenses it’s a real image which is formed at the other side of the lens, and a virtual image is always formed on the same side of the lens as the object. After that however the chapter is remarkably similar to the chapter on spherical mirrors. Why are you advised not to water plants on a bright sunny day? The water forms droplets on the leaves. These droplets act as converging lenses and focus the sun onto the leaves, burning them. As a result the leaves will have brown spots. *Power of a lens The power of a lens is defined as the reciprocal of the focal length in metres. The unit of power is the m–1. Opticians use the dioptre as the name of the unit of power but this is not used in the SI system. *The Eye Did you know that a TV screen shows 24 pictures a second? Because a fly sees 200 images a second, it would see TV as still pictures with darkness in between. Why can we not focus clearly under water yet swimming goggles will restore clear focus? Light refracts when travelling from air through the cornea of your eye, but water and the cornea have the same refractive index (not surprising I suppose – the cornea seems to be mostly water) so light which travels from water to your cornea doesn’t refract much at all, so there is no focusing on the retina. By wearing goggles however light which hits your eye is coming from air, so the usual focusing applies and objects appear normal. Unless you happen to be on a family holiday in Majorca and find yourself underwater staring at Granny’s cellulite arse, in which case ‘normal’ is not the word which first comes to mind. Refractive Index of parts of the eye n cornea = 1.376 n lens = 1.42 n vitreous humour = 1.336 Power of Accomodation RELAXED EYE…. From ∞ to about 6 m objects can be seen clearly…below 6 m lens increases in curvature…it accommodates to give clear image Blind Spot – you know what to do Physics, Art and History Focus an image of a distant object on a screen (a white page) using lenses or mirrors. This is always impressive, particularly when you notice that the image is in colour, and upside down. The lenses must be convex (converging), and the mirrors concave. Why? Some historians of art now believe that from the early 15th century many Western artists including Van Eyck, Caravaggio and Vermeer used mirrors and lenses to create living projections. Optics would have given artists a new tool with which to make images that were both immediate and powerful, enabling them to project colour images onto flat surfaces and then capture these projections in pencil and paint. Upside down glasses The upside-down glasses were first investigated by George Stratton in the 1890’s. Since the image that the retina of our eye sees is inverted, he wanted to explore the effect of presenting to the retina an upright image. He reported several experiments with a lens system that inverted images both vertically and horizontally. He initially wore the glasses over both eyes but found it too stressful, so he decided to wear a special reversing telescope over one eye and keep the other one covered. In his first experiment, he wore the reversing telescope for twenty-one hours. However his world only occasionally looked normal so he ran another experiment where he wore it for eight days in a row. On the fourth day, things

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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 ‘The Focal Point’. When their father asked why they chose that name, they replied, “It’s the place where the sons raise meat”.