Spherical Thin Lenses Optics for Residents Amy Nau

Spherical Thin Lenses Optics for Residents Amy Nau O. D. , F. A. A. O

Spherical Lenses Formulas n Thin lens formula 1/do+1/di=1/f F=1/f 2 n Linear Mag Image size/Object size= di/do n Prentice’s Rule P=F (diopters) xd (cm)

Thin Spherical Lenses n The shape of the refracting surface determines the type of lens and power Object space Image space C 2 C 1 A 1 Object space Image space C 2 A 2 C 1 A 2 Lens is thin if the thickness is small enough not to influence the power All refraction is thus considered to occur in one plane between the two surfaces A 1 front surface vertex; A 2 back surface vertex

Thin Lens Power n n n F 1=nlens-nobject/r and F 2=nimage-nlens/r The total dioptric power of the lens (F) is F 1+F 2 By substitution, another way to write this is : F=(n’-n)/(1/r 1 -1/r 2) This is called the Lens Makers Formula, and it assumes that the surrounding media is air.

Thin Lens Problem n A plastic biconcave lens (n=1. 49) has a surface radii of 40 cm and 20 cm. Calculate the surface and total lens powers. n Solve for F 1 q n Solve for F 2 q n F 1=nlens-nobject/r F 2=nimage-nlens/r Solve for total power q F=F 1+F 2

Image Object Relationships: Position n Assumptions: q q n surrounding media is air Imaging occurs through single plane Formulas q The Gaussian Imaging formula is used to calculate imageobject power relationship n L’=L+F q q q F=total power of the lens Incident vergence (L)=no/l=ns/l=1. 0/l (in air) Emergent vergence (L’)=ni/l’=ns/l’=1. 0/l’(in air) n Where l=object distance and l’=image distance

Object Image Relationships n The types of images and objects as well as sign convention are the same as for single refracting surfaces REAL OBJECTS VIRTUAL IMAGES negative VIRTUAL OBJECTS REAL IMAGES positive

Problem n Virtual image is formed 25 cm from a thin lens. If the object is real and positioned 50 cm from the lens, what is the lens power? n L’=L+F

Image-Object Relationships Focal Points n The primary and secondary focal points are calculated the same was as that for single curved surfaces. Assume the surrounding media is air (n=1) n F=-n/f=n’/f’ becomes F=-1. 0/f=1. 0/f’ The equation shows that for thin lenses f=f’, but they are opposite signs n

Focal Points n n Recall that an infinite axial object forms an image at f’ Recall that an object placed at f, forms an image at infinity

Secondary focal point – convex surface n n’ Object at infinity Secondary focal point F’ f’ secondary focal length (+) Rays converge towards secondary focal point

Secondary focal point –concave surface Rays diverge as if they came from secondary focal point n Secondary focal point Object at infinity F’ f’ secondary focal length (-) n’

Primary focal point n n The object position that yields the image at infinity Emergent vergence (L’) is zero

Primary focal point- positive surface n n’ F C f (primary focal length) F’ (infinity) f’ secondary focal length

Primary focal point – negative surface n’ n Infinite image rays F’ c F f’’ secondary focal length f primary focal length

Problem n What are the primary and secondary focal lengths for a lens (n=1. 49) with a power of -12 D in air? n F=-n/f F=n’/f’

Image-Object Relationships Size and Orientation n This is LATERAL MAGNIFICATION and the ratio is image size/object size q n n n - invereted/+erect These equations are the basis for the lensometer LM=h’/h=nl’/n’l=nsl’/nsl=l’/l LM=-f/x=-x’/f’ (x= extrafocal dist) q Where x=dist from primary focal point to object and x’=dist from seconary focal point to image Just as for single refracting surfaces, set up similar triangles!!!!!!!!!!!

Lateral Magnification xx’=ff’ xx’=-f’f’ xx’=-(f)2 h c c l x l’ f f’ x’ h’

Problem LM n n A real image moves to 5 cm away from a lens when an object is moved from infinity to a position 40 cm in front of the lens. What is the power of the lens? xx’=-(f)2

Distant Object Size n When an object is at an infinite distance, the LM cannot be determined. To solve for the object size use the chief ray tanw=h’/f=-h’/f’ h’=-f’tanw F’ h’ h’ F f f’

Who cares? n The angular subtense of an object as it falls on the retina is used in vision to describe the size of a distant object. q A 20/60 letter on an eye chart subtends a 15 minute arc at 20 feet (1 degree= 60 minutes).

Prismatic Effect of Thin Lenses n The amount of bending after refraction is a function of the distance from the axis q q Closer to the axis bends less This is considered the prismatic effect of a lens The change in direction is the deviation Unlike a prism which has ONE deviation for any incident ray, a lens has an infinite number of deviations

Prismatic Effect of Thin Lenses d 1 d 2 F’ f’

Prismatic Effect of Thin Lenses THERE IS NO PRISMATIC EFFECT AT THE OC OF A LENS However, if the visual axis is not aligjed with the OC there is prism

Prismatic Effect of Thin Lenses The image always shifts Towards the APEX. Positive lenses displace Images opposite the direction Of decentration

Prismatic Effect of Thin Lenses Lens decentered downward = base up. In general, negative lenses displace images In the SAME direction as decentration.

Prismatic Effects n n The magnitude of prismatic deviation in prism diopters is expressed in terms of displacement (cm) and the secondary focal length (m) d=ycm/f’m = ycm. FD

Prism Problem n Patient with PD of 60 mm is given a frame with a 70 mm PD. If the pt’s Rx is -3. 00 D OU, what is the direction and amount of induced prism?

Effective Power n n n Vergence (power) required for a lens at a new position to have the same effect on the incident rays. Becomes important if the distance between a lens and an image plane (retina) is changed. MOVING A LENS AWAY FROM THE IMAGE PLANE INCREASES POSITIVE POWER (DECREASES NEG. POWER)

Effective Power p 1 p 2 screen This is the situation when You move a lens closer (i. e. glasses going to contact Lenses) F’ F’d f’x d d f’ Fx=1/f’-d Fx=F/1 -d. F

Effective Power p 1 p 2 When the lens is moved AWAY, then less power Is required to put the image In the same place CLS to glasses F’ f’ d If lens is moved to the right d is positive, if lens is Moved right to left, d is neg d f’x OR need more bifocal power

Which soldier is taller?

Is it moving and shimmering? Buy a poster! Look at this illusion for a while and it will appear to be shimmering and moving. Also: Follow the outermost groove and watch it change from a groove to a hump as you go around the wheel.

Problem Sets When rays from the sun pass through a convex lens, it makes a bright point image 0. 7 m behind the lens on the ground. n q q What is the focal length of the lens? What is the nature of the image? What is the magnification? What is the power of the lens?

Problem Sets A light bulb is placed 300 cm from a convex lens with a focal length of 50 cm. n q q q Where is the image located? What is the nature of the image? What is the magnification of the image?

Problem Sets A light bulb is placed 300 cm from a convex lens with a focal length of 500 cm. n q q q Where is the image? What is the nature of the image? What is the magnification of the image?

Problem Sets A slide is placed 50 mm from a projector lens and no image is formed. Why? An object of height 7 cm is placed 25 cm in front of a thin converging lens with a focal length of 35 cm. What is the height, location and nature of the image?

Problem Sets Now the object is moved to 90 cm. What is the new image distance, height, and nature of the image?

Problem Sets A patient comes in having trouble with their new glasses which you prescribed. Their acuity is 20/20 in each eye and you determine that the refraction (-5. 50 OD and -2. 50+1. 00 X 090 OS) is accurate. However, the patient reports that they glasses make them uncomfortable. You determine that the lenses have not been centered properly. They are decentered 2 mm out on the OD and 2 mm up on the OS. (how would you do that? ? ). What is the induced prismatic effect?

Problem Sets A patient has a 10 D exophoria at near. The patient needs a +2. 00 D reading add. What amount of prism would you prescribe? How much decentration needs to be added? In what direction is the base of the prism?

Problem Sets A patient with ARMD is having trouble reading. You determine that she needs a +4. 50 add on top of her distance Rx of +1. 00 OU to see the newspaper. How far away does she need to hold the paper to see it clearly? What will be the magnification of an object 10 cm tall held 5 cm from the lens?

Problem Sets An object 0. 08 m high is placed 0. 2 m from a (+) lens. If the distance of the image from the lens is. 40 m, what is the height of the image? Diverging lenses form what kind of images?

Problem Sets An object is placed 0. 2 m from a lens with a focal length of 1. 0 m. How far from the lens will the image be formed?