Week 4 (surfaces, sign convention, surface power, nominal power) (1).docx

Learning outcomes State the definition of a lens and the three general functions it performs Recall the three basic types of surface Define the characteristics of plano, convex and concave surfaces Recall the two basic lens forms and their characteristics List the various types of flat form lenses E...

Learning outcomes State the definition of a lens and the three general functions it performs Recall the three basic types of surface Define the characteristics of plano, convex and concave surfaces Recall the two basic lens forms and their characteristics List the various types of flat form lenses Explain the concept of a steep/flat surface Apply the sign convention to radii of curvature State lens form give front and back surface radii State the unit of refractive power State how the power of a lens relates to focal length Recall the formula for calculating surface power Competently perform calculations of surface power Define the terms optical axis, primary/secondary focal point/focal length Draw and label a diagram to explain the definition of a plus/minus lens Competently calculate the nominal power of a lens from focal length Define the characteristics of a plus/minus/plano lens in terms of thickness, magnification, and image movement Recall which refractive error plus/minus lenses are used to correct State the dioptric increment used within UK optometry Define a thin lens Define nominal power of a lens Competently calculate the nominal power of a lens given surface powers Competently calculate the nominal power of a lens given refractive indices and radii of curvature for surfaces Competently perform spherical lens addition Recommended reading Section 1.1 (‘Preliminary’), 1.2 (‘Sign conventions’), 1.3 (‘Measurement of lens power’), 1.6 (‘Surface power and form’) Principles of ophthalmic lenses, 4th edition, Jalie, ABDO publishing Butterworth Heinemann (https://librarysearch.cardiff.ac.uk/permalink/f/3go6c4/44CAR_ALMA215504024 0002420) Chapter 1 (‘Curvature of surfaces’) in Ophthalmic lenses and dispensing, 3rd edition, Jalie, Butterworth Heinemann (https://librarysearch.cardiff.ac.uk/permalink/f/3go6c4/44CAR_ALMA216895938 0002420) Chapter 18 (‘Spectacle lens design’) and Chapter 21 (‘Aspheric lenses’) Principles of ophthalmic lenses, 4th edition, Jalie, ABDO publishing Butterworth Heinemann (https://librarysearch.cardiff.ac.uk/permalink/f/3go6c4/44CAR_ALMA215504024 0002420) Chapter 1 (‘Focal power’ and ‘Thin lens power’) in Ophthalmic lenses and dispensing, 3rd edition, Jalie, Butterworth Heinemann (https://librarysearch.cardiff.ac.uk/permalink/f/3go6c4/44CAR_ALMA216895938 0002420) Lens Transparent optical medium with two polished surfaces Adds vergence to incident light i.e. spectacle lenses Protect the eye from mechanical/chemical injury i.e. safety lenses Reduce intensity of incident light i.e. sunglasses Lens surfaces 3 basic types of surface: plano, convex, concave Plano Surface is flat Surface does not change the vergence of incident light Surface has zero power Surface has infinitely large radius of curvature Abbreviate as ∞ or write plano Convex Surface bulges (thicker in middle, thinner at edge) Flat edge placed on surface will rock (touches only one point) Surface increases the vergence of incident light (converges light) Surface has plus power E.g. +2.00D lens Concave Surface is hollow (thicker at edge, thinner in middle) Flat edge placed on surface will not rock (touches at two places) Surface decreases vergence of incident light (diverges light) Surface has minus power E.g. -2.00D lens Lens forms Lenses are either flat or meniscus Flat One plano surface with either a convex or concave, or two convex, or two concave Meniscus One convex surface and one concave surface Radius of curvature A surface must be curved to alter vergence of incident light Surface with a long radius of curvature = flat (e.g. beach ball) & lower power Surface with short radius of curvature = steep (e.g. golf ball) & higher power Look at and compare the intersection of the two circles (i.e. the golf ball and the beach ball) Smaller radius has a steeper curve, larger radius has a flatter curve As the radius tends to infinity, the surface flattens Calculating curvature The angle through which the surface turns in a unit length of arc Equation 1 Formula for calculating curvature (R), where r is the radius in metres. The units of curvature are m-1. Sign convention for radii or curvature Lens is treated as the origin (Cartesian coordinates) Think of this as a number scale with a 0 centred on the lens Everything to left of the lens = negative values Everything to the right of the lens = positive value negative radius of curvature = centre of rotation lies to the left positive radius of curvature = centre of rotation lies to the right Biconvex lens Front surface has a positive radius of curvature – centre lies to the right of lens Back surface has a negative radius of curvature – centre lies to the left of the lens Biconcave lenses Front surface has a negative radius of curvature – centre lies to the left of lens Back surface has a positive radius of curvature – centre lies to the right of the lens Meniscus lens Front surface has a positive radius of curvature Back surface has a positive radius of curvature E.g. what is the curvature of a sphere with a radius of +50cm? +50cm = +0.5m, R = 1 +0.5 = +2m-1 Refractive power/lens power The unit of measurement of the refractive power of a lens or a surface is the dioptre, denoted as D (DS for dioptre sphere, DC for dioptre cylinder) The power of a lens (in dioptres) is the reciprocal of the focal length of a lens (see definition of minus and plus lenses in lecture 3) Note that unit of lens power is the same as for vergence Lenses are numbered according to how much vergence they add to light* E.g. a +2.00D lens adds +2.00D of vergence to light E.g. a -2.00D lens adds -2.00D of vergence to light * it is fine to begin to think of lenses in this way, but later when dealing with thick lenses, you will see that lenses are numbered according to back vertex power (BVP) which is the vergence of light leaving the back surface Calculating the surface power of a lens Spectacle lenses have 2 surfaces Front surface Since light travels left to right, light is travelling in air (n) and then enters the medium of the lens (n’) through the front surface of the lens Back surface Since light travels left to right, light is travelling in the medium of the lens (n) and then exits through the back surface of the lens into air (n’) Important to note what optical medium light is currently in and what it will be entering. Formula for calculating surface power, where F is the power in dioptres (D), n is the refractive index of the incident medium (what light is going from), n' is the refractive index of the refracting medium (what light is going into), r is the radius of curvature of the surface in metres. e.g. You pick up a lens in the lab. What is the back surface power of this lens if it is made of glass (n=1.500) with a back surface radius of +0.50m? e.g. You pick up a lens in the lab. What is the front surface power of this lens if it is made of glass (n=1.500) with a front surface radius of +0.50m? Again, you do not need to work in metres, you can work in centimetres and millimetres if you choose, but you must use the correct correction If you want to work in cm: If you want to work in mm: Lens terminology Optical axis An imaginary line that is perpendicular to both sides of the lens Light passes through the optical axis undeviated Thin plus lens E.g. could be a plano-convex, equi-convex, bi-convex, or positive meniscus lens A thin plus lens adds positive vergence to light rays When defining plus lenses, we must always ensure incident vergence is zero (i.e. parallel rays) Light rays leaving the lens will now have a positive vergence (i.e. they are now converging) Light rays enter lens with 0.00D vergence Lens adds +4.00D vergence to light rays Light rays leave the lens with +4.00D vergence The secondary focal point (F’) The point on the optical axis where incident light (zero vergence) leaves the lens (positive vergence) and then crosses the optical axis A positive secondary focal length (f’) Remember the sign convention, the lens is the reference point Distances to the right of the lens are positive Plus lenses have a positive secondary focal point A positive secondary focal point is real Rays of light will actually cross there The distance from the secondary focal point (F’) to the lens is the secondary focal length (f’). In the above diagram light with zero vergence (i.e. parallel light) is entering the lens. The lens then adds positive vergence and the light leave the lens. The light rays are now converging and cross at point F’, the secondary focal point. The distance from the secondary focal point to the lens is the secondary focal length, f’. The primary focal point (F) The point on the optical axis where rays diverging from a source would have zero vergence when they exit the lens (i.e. rays are parallel when they leave the lens) Note that the presence/absence of the prime symbol (‘) denotes whether light has travelled through a lens or not F’ = secondary focal point i.e. after light has travelled through the lens F = primary focal point i.e. before light has travelled through the lens Thin minus lens E.g. could be a plano-concave, equi-concave, bi-concave, or negative meniscus lens A thin minus lens adds negative vergence to light rays When defining minus lenses, we must always ensure incident vergence is zero (i.e. parallel rays) Light rays leaving the lens will now have a negative vergence (i.e. they are now diverging) Light rays enter lens with 0.00D vergence Lens adds -4.00D vergence to light rays Light rays leave the lens with -4.00D vergence The secondary focal point (F’) The point on the optical axis where light rays would have emerged if they were to have the observed amount of vergence A negative secondary focal length (f’) Remember the sign convention, the lens is the reference point Distances to the left of the lens are negative Minus lenses have a negative secondary focal point A negative secondary focal point is virtual Rays of light do not actually emanate from there The distance from the secondary focal point (F’) to the lens is the secondary focal length (f’) In the above diagram light with zero vergence (i.e. parallel light) is entering the lens. The lens then adds negative vergence and the light leave the lens. The light rays are now diverging. Tracing the rays back in a straight line would suggest they were emanating from the point F’, the secondary focal point. The distance from the secondary focal point to the lens is the secondary focal length, f’. The primary focal point (F) The point on the optical axis where rays are converging towards so that they would emerge from the lens with zero vergence (i.e. rays are parallel when they leave the lens) Again, note that the presence/absence of the prime symbol (‘) denotes whether light has travelled through a lens or not F’ = secondary focal point i.e. after light has travelled through the lens F = primary focal point i.e. before light has travelled through the lens Focal length of a thin lens Recall that the definition of focal length requires zero vergence Zero vergence entering the lens (secondary focal length f’) Zero vergence leaving the lens (primary focal length f) Thus, by examining the vergence of light entering or leaving the lens, we can work out how much vergence the lens adds to the lens (i.e. the total power of the lens) For example, suppose a thin lens has a secondary focal length of +20cm, what can we say about this lens? The use of the term secondary focal length implies that light rays entered the lens with zero vergence. The lens added positive vergence since the secondary focal length is positive What is the vergence that corresponds to +20cm? In other words, the lens added +5.00D of vergence The total power of the lens is therefore +5.00D Total lens power and focal length The previous section allows us to calculate the total lens power from the focal length (note that I am using the general term ‘focal length’ but in reality, I mean secondary focal length). The total power of a lens (F) is related to its focal length (f): Equation 2 Formula for calculating the focal length of a lens in metres. Replace the value of 1 with n of the desired optical media. If the lens is in air Again, you do not need to use metres, but remember to apply the appropriate correction E.g. if working in cm: E.g. if working in mm: E.g. what is the total power of a lens that has a focal length of +5cm? Plano lens A lens with no power should be called ‘afocal’ However, this type of lens is commonly known as a plano lens Misnomer – consider a plano meniscus lens both surfaces are curved! Minus lenses Thicker at the edge than at the centre With movement Image moves in the same direction as lens movement, relative to the object Minify Image is smaller Correct myopia (“short-sightedness”) Plus lenses Thicker at the centre than at the edge Against movement Image moves in the opposite direction as lens movement, relative to the object Magnify Image is bigger Correct hypermetropia (“long-sightedness”) Plano lenses Same thickness at edge and centre No movement No magnification/minification Standard dioptric increments Lens power is expressed in 0.25D increments E.g. for plus power o +0.25D “plus oh-two-five” o +0.50D “plus oh-fifty” o +0.75D “plus oh-seven-five” E.g. for minus power -1.25D “minus one-two-five” -1.50D “minus one-fifty” -1.75D “minus one-seven-five” Two decimal places If a lens has plano sphere, can write Plano ±0.00DS ꚙ (infinity symbol) Thin lenses A lens where the thickness is negligible What we have been considering up until this point Nominal power formula/thin lens formula Nominal power is the combined (i.e. total) power of the front and back surfaces of a lens On a meniscus lens we normally refer to the convex surface as the front surface As this is a thin lens, we ignore the thickness Nominal power (F) can be calculated from F1 (power of the front surface), and F2 (power of the back surface): E.g. consider the following lens The lens depicted above will have a nominal (i.e. total) power of +2.00D This lens would have a focal length of +0.50m/+50cm/500mm Lens makers equation Relates power nominal power of a thin lens to refractive index and radius of curvature Formula for calculating the nominal power of a thin lens using refractive index and radius of curvature, where n’ = medium light is entering, n = medium light is leaving, r1 = radius of curvature of front surface, r2 = radius of curvature of back surface. Note that the formula above is just the formula for the surface powers added to one another E.g. what is the total power of a crown glass meniscus lens made with a front surface curve of radius +10cm and a back surface curve of radius +20cm? Spherical lens addition Thin lenses can be added to one another e.g. a thin lens with a nominal power of +2.00D lens placed in contact with a thin lens with a nominal power of +3.00D is equivalent to a single +5.00D thin lens Have a go After the webinar, you should attempt the following computer scripts Focal length to dioptres The are many more examples in the recommended reading/related textbooks with answers if you wish to get more practice at other types of question