11

Chapter 4 & 3Chapter 4 & 3Lenses & Lenses & ReflectionReflection

Types of LensesTypes of Lenses Converging: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

Answer: Page 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 of being refracted very much. The optical power of the lens is weak.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?

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 and Radii of curvature are positive for converging lenses and

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

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

negative when inverted.negative when inverted. Answer: Page 122, Q. 5,6,7,9Answer: Page 122, Q. 5,6,7,9

Devices: CameraDevices: Camera

Eye BallEye Ball

RefractionRefraction Refraction is the bending of light as it Refraction is the bending of light as it

changes speed as it passes from one changes speed as it passes from one medium to another.medium to another.

The angle is measured from the normal.The angle is measured from the normal. Light bends towards the normal if Light bends towards the normal if

it enters an optically denser it enters an optically denser substance and v.v.substance and v.v.

Table of ObservationsTable of Observations# Activity1 Invisible coin

2 Broken pencil3 Glass block

4 From air to water

5 From water to air6 Dispersion of light

7 Light ray thru’ glass

Observations 1.1. Coin disappears when Coin disappears when

viewed from sideviewed from side2.2. Pencil appears to bendPencil appears to bend3.3. Coin disappears when Coin disappears when

viewed from sideviewed from side4.4. Light bends as it enters Light bends as it enters

containercontainer5.5. Light bounces off waterLight bounces off water6.6. Light spreads out into Light spreads out into

colours ROYGBVcolours ROYGBV7.7. Light bends twice as it Light bends twice as it

enters and exits the glassenters and exits the glass

Refractive Index - nRefractive Index - n The refractive index, n, is a measure of how The refractive index, n, is a measure of how

much light bends as it enters the substance.much light bends as it enters the substance. n = c/v, where c = 3x10n = c/v, where c = 3x108 8 m/sm/s v = velocity of light in new mediumv = velocity of light in new medium Air has a refractive index of 1.Air has a refractive index of 1. Diamond bends light the most (n= 2.42).Diamond bends light the most (n= 2.42). Table of n values – page 79.Table of n values – page 79.

1717

Snell’s LawSnell’s Law In air, n = sin ΘIn air, n = sin Θi i / sin Θ/ sin Θ r r

Snell’s Law: nSnell’s Law: n11sinΘsinΘ11 = n = n22sinΘsinΘ22

The left side refers to the medium in which the light is The left side refers to the medium in which the light is incident.incident.

The right side refers to the medium to where the light The right side refers to the medium to where the light exits.exits.

ActivityActivity P. 81, Q. 1-3P. 81, Q. 1-3 P. 83, Q. 1-2P. 83, Q. 1-2 P. 86, Q. 3-5, 7P. 86, Q. 3-5, 7

1818

Total Internal ReflectionTotal Internal Reflection This occurs when a ray of light passes This occurs when a ray of light passes

from an optically dense material (big n) to from an optically dense material (big n) to an optically LESS dense material (low n).an optically LESS dense material (low n).

If the angle of incidence is greater than a If the angle of incidence is greater than a certain angle – the critical angle - the certain angle – the critical angle - the light will NOT refract out, but will reflect light will NOT refract out, but will reflect internally.internally.

1919

TOTAL INTERNAL REFLECTION TOTAL INTERNAL REFLECTION (TIR)(TIR)

Critical AngleCritical Angle In TIR situations, there comes a point at which the In TIR situations, there comes a point at which the

angle of refraction increases until it leaves the angle of refraction increases until it leaves the medium.medium.

In this case the angle of refraction can be considered In this case the angle of refraction can be considered to be equal to 90to be equal to 90oo..

The angle of incidence at which an angle of refraction The angle of incidence at which an angle of refraction of 90° first occurs is the Critical Angle.of 90° first occurs is the Critical Angle.

Thus for Critical Angle questions, the angle of Thus for Critical Angle questions, the angle of refraction is assumed to be 90°.refraction is assumed to be 90°.

2121

Total Internal ReflectionTotal Internal Reflection

2222

Snell’s Law & TIRSnell’s Law & TIR nn11sinΘsinΘ11 = n = n22sinΘsinΘ2 2

Thus the ΘThus the Θ2 2 is 90is 90oo, always., always. The ΘThe Θ1 1 is called Θis called Θc c , the critical angle., the critical angle. As n increases, the ΘAs n increases, the Θcc decreases causing decreases causing

more TIR, which is why diamonds appear so more TIR, which is why diamonds appear so brilliant.brilliant.

Page 88, Q. 1, 2, 6Page 88, Q. 1, 2, 6

2323

Fibre OpticsFibre Optics This is especially useful in fibre optics.This is especially useful in fibre optics. Light enters a optic fibre and reflects on Light enters a optic fibre and reflects on

the inside of the cable instead of the inside of the cable instead of escaping.escaping.

So signals can be transmitted at the So signals can be transmitted at the speed of light, much faster than the speed of light, much faster than the speed of electricity.speed of electricity.

2424