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Physics. PHS 5041 Optics Lenses. PHS 5041 Optics Lenses. Lenses are transparent objects with at least one curved surface. Lenses can be: _Convex or converging (*** thickest at the centre ) (double convex, plano -convex, concavo-convex) _Concave or diverging

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phs 5041 optics lenses1
PHS 5041 OpticsLenses

Lenses are transparent objects with at least one curved surface.

Lenses can be:

_Convex or converging (***thickest at the centre)

(double convex, plano-convex, concavo-convex)

_Concave or diverging

(double concave, plano-concave, convexo-concave

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PHS 5041 OpticsLenses

XY: principal axis of lens

O: optical centre of lens

F: principal focus of length

F’: secondary principal focus of length

OF or OF’: focal length

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PHS 5041 OpticsLenses

Lenses behave like prims, but with varying incident angles

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PHS 5041 OpticsLenses

Lenses behave like prims, but with varying incident angles

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PHS 5041 OpticsLenses

Principal rays: Rays for which we do not need to measure angle in order to determine their direction after reflection.

There are 3 types of principal rays (converging lens)

1: Incident ray parallel to principal axis

2: Incident ray passing through secondary focus

3: Incident ray passing through optical centre

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PHS 5041 OpticsLenses

Drawing images formed by lenses:

We use the three principal rays (whenever feasible) for both type of lenses, and according to the position of the object

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

***When the object is at infinity, the image is a dot, and it is located at F (principal focus of length)

Object between ∞ and 2F’,

Image is:

_Real

_Between F and 2F

_Inverted

_Smaller

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

Object at 2F’,

Image is: Real, at 2F, Inverted, Same size

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

Object between 2F’ and F’,

Image is: Real, after 2F, Inverted, Larger

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

Object at F’,

NO Image

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

Object between F’ and O,

Image is: Virtual, between F’ and O, Upright, Larger

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

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PHS 5041 OpticsLenses

Drawing images (Converging lenses):

Converging lenses DO NOT produce images between F and O

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PHS 5041 OpticsLenses

Practice:

_The image of a slide on a screen is larger, upright and real (seen on screen).

  • Should the slide be upright or inverted when placed in the projector?
  • Where should the slide be located with respect to the lens?
  • Where should the screen be placed with respect to the lens?

Inverted

Between F’ and 2F’

Between 2F and ∞

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PHS 5041 OpticsLenses

Practice:

_To photograph an object located at infinity, should the principal focus of the lens be located in front, behind or on the film? Hint: the film is the screen.

_To photograph an object close to the camera, should the principal focus of the lens be located in front, behind or on the film? Hint: the film is the screen.

F should be located on the film(object-lens-F/film), for objects at infinity produce images at F

F should be located in front of the film (object-lens-F-film), for converging lenses do not produce images between F and O

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PHS 5041 OpticsLenses

Principal rays: Rays for which we do not need to measure angle in order to determine their direction after reflection.

There are 3 types of principal rays (diverging lens)

1: Incident ray parallel to principal axis

2: Incident ray directed to the secondary focus

3: Incident ray passing through optical centre

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PHS 5041 OpticsLenses

Drawing images (Diverging lenses):

***When the object is at infinity, the image is a dot, and it is located at F (principal focus of length)

Object between ∞ and F,

Image is:

_Virtual

_Between F and O

_Upright

_Smaller

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PHS 5041 OpticsLenses

Drawing images (Diverging lenses):

Object at F,

Image is: Virtual, between F and O, Upright, Smaller

phs 5041 optics lenses22
PHS 5041 OpticsLenses

Drawing images (Diverging lenses):

Object at F and O,

Image is: Virtual, between F and O, Upright, Smaller

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PHS 5041 OpticsLenses

Drawing images (Diverging lenses):

Diverging lenses ONLY produce images between F and O

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PHS 5041 OpticsLenses

Images

(Converging lenses):

_Never between F and O

_Real, inverted, and behind lens (converging refracted rays)

_Virtual, upright, in front of lens (diverging refracted rays)

_No image (parallel diffracted rays)

Images

(Diverging lenses):

_Always between F and O

_Always upright, virtual and smaller

_Object moving from infinity, images grows from dot at F to same size very near to lens

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PHS 5041 OpticsLenses

Calculations:

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PHS 5041 OpticsLenses

Example:An object 1cm high is placed 27 cm from a convex lens with focal length of 18 cm. At what distance from the mirror is the image formed and what is the height, type and orientation?

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PHS 5041 OpticsLenses

Example:An object 1cm high is placed 27 cm from a convex lens with focal length of 18 cm. At what distance from the mirror is the image formed and what is the height, type and orientation?

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PHS 5041 OpticsLenses

Optical power: Capacity of a lens to bend light rays

L1

L1

L3

Proportionality between f and P?

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PHS 5041 OpticsLenses

Optical power: Capacity of a lens to bend light rays

P = 1 / f

P: Optical power (d: diopters)

f: focal length (m: meters)

P > 0 (converging lens)

P < 0 (diverging lens)

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PHS 5041 OpticsLenses

Optical power of a system of lenses:

Pt = P1 + P2 + … + Pn

P: Optical power (d: diopters)

f: focal length (m: meters)

Pt > 0 (converging system of lens)

Pt < 0 (diverging system of lens)

n lenses

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PHS 5041 OpticsLenses

Example: Find the optical power of a system of lenses whose individual focal lengths are 0.20 m, 0.10 m and -0.05m respectively. Is the system of lenses converging or diverging?

P = 1/f Pt = P1 + P2 + P3

P1 = 1 / 0.20m Pt = 5d + 10d – 20d

P1= 5d

P2 = 1 / 0.10m Pt= - 5d (Diverging system, P < 0)

P2 = 10d

P3 = 1 / -0.05m

P3 = -20d

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PHS 5041 OpticsLenses

Lens maker equation:

P = (n – 1) (1 / R1 + 1 / R2)

P: Optical power (d: diopters)

n: index of refraction of lens material

R1 & R2: radii of curvature of each side of the lens (m: meters)

R1 & R2 > 0 (converging lenses)

R1 & R2< 0 (diverging lenses)

P > 0 (converging lens)

P < 0 (diverging lens)

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PHS 5041 OpticsLenses

Example: A plastic lens with index of refraction 1.51 is composed of two convex lenses with radius of curvature 5 cm on each side. Find the optical power of a system of lenses. Is the system of lenses converging or diverging?

P = (n – 1) (1 / R1 + 1 / R2)

P = (1.51 – 1) (1 / 0.05m + 1 / 0.05m)

P = (0.51) (40) d

P = 20.4 d (Converging system, P > 0)

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PHS 5041 OpticsLenses

Human eye:

_Sclerotic: opaque membrane that protects the eye

_Cornea: transparent membrane

_Lens: converging lens

_Ciliary muscles: Exert pressure on lens, thus changing its F (accommodation). This allows for near and distant vision

_Retina: back of the eye (screen)

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PHS 5041 OpticsLenses

Nearsightedness (Myopia):

Difficulty seeing distant objects

Possible causes:

_Eyeball is too long

_Cornea is too curved

Evidence: Image is formed in front of the retina

Correction: Eyeglasses or contact glasses with diverging lenses

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PHS 5041 OpticsLenses

Farsightedness (Hyperopia):

Difficulty seeing nearby objects

Possible causes:

_Eyeball is too short

Evidence: Image is formed behind the retina

Correction: Eyeglasses or contact glasses with converging lenses

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PHS 5041 OpticsLenses

Presbyopia:

Difficulty adjusting the focal length of lens (due to aging)

Possible causes:

_Ciliary muscles lose some of their elasticity

Evidence: Image is formed behind the retina

Correction: Eyeglasses or contact glasses with converging lenses

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PHS 5041 OpticsLenses

Astigmatism:

Difficulty focusing on both plans (horizontal and vertical) at the same time

Possible causes:

_Differences in curvature of the lens of the eye

Evidence: Eye focuses better in one plane than in the other

Correction: Eyeglasses with cylindrical lenses

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PHS 5041 OpticsLenses

Other defects

Strabismus: Misalignment of eyeballs. Prevents combination of images formed by both eyes

Pigmentary glaucoma: Excessive pressure in liquid substances of eyeball. Destroys optic nerve, leads to blindness

Cataracts: Lens becomes opaque. People cannot see near or distant objects (need bifocals: diverging and converging lenses)

Colour blindness: Rods in the retina are insensitive to colours.