Physics 504Physics 504Chapter 4Chapter 4LensesLenses

Types of Lenses

Converging:: Causes light rays to come together Causes light rays to come together Examples: Magnifying glass, camera, eye Examples: Magnifying glass, camera, eye

glasses glasses

Diverging:Diverging: Causes light rays to spread apart Causes light rays to spread apart Examples: Microscope, telescope, eye Examples: Microscope, telescope, eye

glasses glasses

Principal RaysPrincipal Rays Just like curved mirrors, lenses are used to Just like curved mirrors, lenses are used to

produce imagesproduce images The images are found by using three principal The images are found by using three principal

rays:rays: Principal Ray 1: Principal Ray 1: A light ray parallel to the principal A light ray parallel to the principal

axis is refracted through the principal focal point.axis is refracted through the principal focal point. Principal Ray 2: Principal Ray 2: Passes through the optical center. Passes through the optical center.

No apparent refraction occurs but the ray is bent. No apparent refraction occurs but the ray is bent. The ray seems to pass straight through to the other The ray seems to pass straight through to the other side.side.

Principal Ray 3:Principal Ray 3: Passes through the secondary Passes through the secondary focal point and will be refracted. Will exit the lens focal point and will be refracted. Will exit the lens parallel to the principal axis.parallel to the principal axis.

Converging LensConverging Lens

LensLens

Diverging LensesDiverging Lenses

Principal ray 1Principal ray 1 (parallel to the principal axis, (parallel to the principal axis, PA) will be refracted away from the PA) will be refracted away from the PAPA. But the . But the prolongation of the ray will pass through the prolongation of the ray will pass through the principal focus.principal focus.

Principal ray 2Principal ray 2 (straight through the optical (straight through the optical center) has no apparent sign of refraction.center) has no apparent sign of refraction.

Principal ray 3Principal ray 3 (via the secondary focal point) (via the secondary focal point) is refracted parallel to the principal axis. is refracted parallel to the principal axis.

Diverging LensDiverging Lens

ActivityActivity

Page 98, Q. 1-3Page 98, Q. 1-3

Optical PowerOptical Power

The strength of a lens (optical power) is related The strength of a lens (optical power) is related to its focal length. A short focal length means to its focal length. A short focal length means the light rays are being refracted a lot. The the light rays are being refracted a lot. The optical power of the lens is strong.optical power of the lens is strong.

A long focal length means the light rays are not A long focal length means the light rays are not being refracted very much. The optical power being refracted very much. The optical power of the lens is weak.of the lens is weak.

The power of a lens is equal to the inverse of The power of a lens is equal to the inverse of the focal point. P = 1/fthe focal point. P = 1/f

Power unit: dioptres (d)Power unit: dioptres (d) Focal length: meters (m), negative if divergingFocal length: meters (m), negative if diverging

Lens CombinationsLens Combinations

By combining lenses, different optical powers can be By combining lenses, different optical powers can be obtained. This is quite useful for making telescopes, obtained. This is quite useful for making telescopes, microscopes or any other optical instrument that uses microscopes or any other optical instrument that uses more than one lens. more than one lens.

The The optical powersoptical powers can be added using the equation: can be added using the equation: PPTT = P = P11 + P + P22 + P + Pnn…… PPTT: Total optical power in dioptres: Total optical power in dioptres PP11, P, P22, P, Pnn,: Power of each lens in dioptres. ,: Power of each lens in dioptres. N.B. N.B. The focal lengths The focal lengths CAN NOTCAN NOT be added together to be added together to

solve optical power. You must use the equation solve optical power. You must use the equation P=1/fP=1/f to to obtain the obtain the PP value. value.

Lens CombinationsLens Combinations

What is the power, focal lengths?What is the power, focal lengths?

ActivitiesActivities

Page 112, Q. 2-3, 5Page 112, Q. 2-3, 5 Testing your knowledgeTesting your knowledge

Thin Lens Thin Lens EquationsEquations

ddoo is the distance to the object is the distance to the object

ddii is the distance to the image is the distance to the image

f is the focal lengthf is the focal length hhii is the image height is the image height

hhoo is the object height is the object height

N.B. the negative signN.B. the negative sign

Conventions for the Conventions for the EquationEquation Distances are measured from the vertex.Distances are measured from the vertex. Focal lengths are positive for converging lenses and Focal lengths are positive for converging lenses and

negative for diverging lensesnegative for diverging lenses Radii of curvature are positive for converging lenses Radii of curvature are positive for converging lenses

and negative for diverging lenses.and negative for diverging lenses. Image and object distances are positive for real Image and object distances are positive for real

images and objects.images and objects. Image and object distances are negative for virtual Image and object distances are negative for virtual

images and objects.images and objects. Image and object heights are positive when upright Image and object heights are positive when upright

and negative when inverted.and negative when inverted.

ActivityActivity

Page 122, Q. 5,6,7,9Page 122, Q. 5,6,7,9

Devices that Use LensesDevices that Use Lenses

Many devices rely on lenses, but what is Many devices rely on lenses, but what is a lens? a lens?

Circular in shape Circular in shape Made of transparent material Made of transparent material When light rays pass through it, they are When light rays pass through it, they are

refracted (change direction) refracted (change direction)

Devices: CameraDevices: Camera

Eye BallEye Ball

SummarySummary Curved lens terms: optical centre, principal Curved lens terms: optical centre, principal

axis, principal focus, focal length, focal axis, principal focus, focal length, focal plane.plane.

A lens’ focal length is the distance between A lens’ focal length is the distance between the optical centre and the principal focus the optical centre and the principal focus measured along the principal axis.measured along the principal axis.

The rules for rays in curved lenses are:The rules for rays in curved lenses are: A ray parallel to the principal axis is refracted so A ray parallel to the principal axis is refracted so

that it passes thru’ (or appears to pass thru’ the that it passes thru’ (or appears to pass thru’ the principal focus. (F).principal focus. (F).

A ray passing thru’ (or appearing to pass thru’) A ray passing thru’ (or appearing to pass thru’) the secondary principal focus (F’) is refracted the secondary principal focus (F’) is refracted parallel to the principal axis.parallel to the principal axis.

A ray passing thru’ the optical centre goes A ray passing thru’ the optical centre goes straight thru’, without bending.straight thru’, without bending.

Converging lenses and their combinations Converging lenses and their combinations are used as magnifying glasses, spotlights, are used as magnifying glasses, spotlights, projectors, cameras, telescopes, binoculars, projectors, cameras, telescopes, binoculars, and microscopes, glasses.and microscopes, glasses.

Diverging lenses are used in glasses.Diverging lenses are used in glasses. Dispersion causes chromatic aberration in Dispersion causes chromatic aberration in

lenses. This defect can be partially lenses. This defect can be partially corrected by using 2 or more lenses with corrected by using 2 or more lenses with different optical densities. different optical densities.

P = 1/f, f in metres, P in dioptres.P = 1/f, f in metres, P in dioptres. Powers made be summed. PPowers made be summed. PT = P = P11+ P+ P22 +… +…

ActivityActivity

Page 130, Q. 3`, 9Page 130, Q. 3`, 9