Physics. PHS 5041 Optics Lenses Lenses are transparent objects with at least one curved surface....

Physics

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


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


Lenses behave like prims, but with varying incident angles


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


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


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



Object at 2F’,

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



Object between 2F’ and F’,

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



Object at F’,

NO Image



Object between F’ and O,

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



Converging lenses DO NOT produce images between F and O


Practice:

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

a) Should the slide be upright or inverted when placed in the projector?

b) Where should the slide be located with respect to the lens?

c) Where should the screen be placed with respect to the lens?

Inverted

Between F’ and 2F’

Between 2F and ∞


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 lens produce images at F


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



***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



Object at F,

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



Object at F and O,

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



Diverging lenses ONLY produce images between F and O


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


Calculations:


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?


Optical power: Capacity of a lens to bend light rays

L1

L1 L3

Proportionality between f and P?


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)


Optical power of a system of lenses:

Pt = P1 + P2 + … + Pn


f: focal length (m: meters)

Pt > 0 (converging system of lens)

Pt < 0 (diverging system of lens)

n lenses


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 – 20dP1= 5d

P2 = 1 / 0.10m Pt = - 5d (Diverging system, P < 0)P2 = 10d

P3 = 1 / -0.05m P3 = -20d


Lens maker equation:

P = (n – 1) (1 / R1 + 1 / R2)


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)


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


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)


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


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


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


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


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.

Physics. PHS 5041 Optics Lenses Lenses are transparent objects with at least one curved surface....

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