Optics Course (Phys ) Geometrical Optics Refraction through Lenses Lecturer: Dr Zeina Hashim
Slide 1 Objectives covered in this lesson : 1. Refraction through single spherical refracting surfaces. 2. Lenses: converging and diverging. 3. Lenses: thin and thick. 4. Refraction through thin spherical lenses. 5. Lateral Magnification.
Slide 2 Images [from Refracting Surfaces] : Virtual Images They are images which require the visual system of an observer. They form on the same side of a lens where the object is. They form when the rays are redirected away from the central axis. They form when the backward extensions of the object s redirected rays cross. Real Images They are images which can form on a surface & can exist even if no observer is present. They form on the opposite side of a lens of where the object is. They form when the rays are redirected towards the central axis. They form when the redirected rays cross.
Slide 3 Refraction through Single Spherical Refracting Surfaces : Plane surfaces: angle of incidence normal angle of reflection Spherical surfaces: Convex: Concave: θ 1 θ 1 n 1 air n 2 θ 2 angle of refraction glass in 6 cases Assume: Snell s Law Medium with high (n) is shaded. Object O is always in the medium of n 1, at the left of the figure. n 2 sin θ 2 = n 1 sin θ 1 C is the center of curvature.
Slide 4 Refraction through Single Spherical Refracting Surfaces : 6 possible cases Case 1 & 2 Convex + Object far from Surface Rays are refracted towards the central axis & real images are formed
Slide 5 Refraction through Single Spherical Refracting Surfaces : 6 possible cases Case 3 & 4 Convex + Object near the Surface Rays are refracted away from the central axis & virtual images are formed
Slide 6 Refraction through Single Spherical Refracting Surfaces : 6 possible cases Case 5 & 6 Concave + Regardless of object distance Rays are always refracted away from the central axis & virtual images are always formed
Slide 7 Refraction through Single Spherical Refracting Surfaces : For light rays making only small angles with the central axis: n 1 + n 2 p i = n 2 n 1 r single spherical refracting surfaces n 1 = index of refraction where the object is. n 2 = index or refraction of other material. p = object distance from mirror. (p always positive). i = image distance from mirrors. (i is negative virtual image, positive real image). r = radius of curvature (is negative object faces a convex, positive object faces a concave). Study Sample Problem 34-2 in Halliday (8 th ed.) to get familiar with how to use this equation.
Slide 8 Refraction through Single Spherical Refracting Surfaces : Vote: A bee is hovering in front of the concave spherical refracting surface of a glass sculpture: Group Activity (a) Which of the general situations (see figures) is like this situation? (b) Is the image produced by the surface real or virtual? (c) Is it on the same side as the bee or the opposite side?
Slide 9 Lenses : A lens: is a refracting device: it is a transparent object with two refracting surfaces whose central axes coincide. Placing an object in front of the a lens an image is produced from the refracted rays (or their extensions).
Slide 10 Types of Lenses : Converging lens Also called: Convex lens, Positive lens. is a lens that can bring parallel light beam passing through it to a point. Diverging lens Also called: Concave lens, Negative lens. is a lens that causes a beam of parallel light to diverge.
Slide 11 Types of Lenses : Converging lens Diverging lens
Slide 12 Types of Lenses : A thin lens is a lens whose thickness is small compared with: the object distance p. the image distance i. the radii of curvature r 1 & r 2 of the two surfaces of the lens. A thick lens is a lens whose thickness is not negligible.
Slide 13 Understanding Parameters of Thin Lenses: Centres and Radii of curvature Principle axis Also called optical axis Optical Centre Radii in Halliday with the approximation (thin lenses): both are right Radii in Hecht
Slide 14 Understanding Parameters of Thin Lenses: Focal Points, lengths, planes Focal points of lenses are defined in terms of their effect on parallel light rays and plane wave fronts. Lenses have two focal points. Real F Virtual F Focal length (from optical centre to focal point) is approximated to be the same on both sides of a thin lens.
Slide 15 Understanding Parameters of Thin Lenses: Focal Points, lengths, planes Focal plane: a lens will focus all incident parallel bundles of rays onto a surface called the second or back focal plane.
Slide 16 Understanding Parameters of Thin Lenses: Object and image distance
Slide 17 Refraction through thin lenses: When the thin lens is in air: n medium = n air 1 1 p + 1 i = n lens 1 1 r 1 1 r 2 : n lens n medium Lensmaker s Formula (Thin-lens equation) If the lens is in another medium: replace n lens in the equation with r 1 = radius of curvature of the lens surface nearer the object. r 2 = radius of curvature of the other surface. 1 p + 1 i = 1 f n lens n medium Thin lenses Q: Lenses have two focal points. Which focal length do we use in the equation?
Slide 18 Refraction through thin lenses: Study Sample Problem 34-4 in Halliday (8 th ed.) to get familiar with how to use the lens equation.
Slide 19 Refraction through thin lenses: Group Work In groups of 2: Parallel rays of red light that are directed at a converging lens are focused at a point P on the central axis to the right of the lens when the lens is surrounded by air as shown. If the lens is surrounded by water instead of air, where will the red parallel rays be focused relative to point P? a) above point P b) below point P c) to the left of point P d) to the right of point P e) at point P.
Slide 20 How to easily draw rays with a lens: O outside F O inside F Convex lens: 3 rays O anywhere Concave lens:
Slide 21 Refraction through thin lenses: Group Work In groups of 2: A physics student desires to create a beam of light that consists of parallel rays. Which one of the following arrangements would allow her to accomplish this task? a) A light bulb is placed at the focal point of a convex mirror. b) A light bulb is placed at the focal point of a diverging lens. c) A light bulb is placed at the focal point of a converging lens. d) A light bulb is located at twice the focal length from a concave mirror. e) A light bulb is located at twice the focal length from a converging lens.
Slide 22 Refraction through thin lenses: Group Work In groups of 2: If the student then places a hairclip instead of the light bulb in that same position. Where will the image of the hairclip appear? a) no image will be formed. b) the image will be at a distance greater than f to the left of the lens, and will be inverted. c) the image will be at a distance greater than f to the right of the lens, and will be upright. d) the image will be at a distance f/2 to the right of the lens, and will be inverted. e) the image is at a distance f/2 to the left of the lens, and will be upright.
Slide 23 Lateral Magnification : The lateral magnification is determined by one of the following equations: m = i p m = h h where h and h are the heights of the object and its image (measured perpendicular to the central axis), respectively. When m is positive object and image have the same orientation. When m > 1 image > object. When m < 1 image < object.
Slide 24 Refraction through thin lenses: Group Work In groups of 2: An object is placed at a distance 5.0 cm to the left of a diverging lens with a focal length 2.5 cm. Using the thin lens equation and the magnification equation, determine the location and magnification of the image formed by this configuration. a) The image is formed 1.7 cm to the left of the lens and it has a magnification of +1/3. b) The image is formed 0.6 cm to the left of the lens and it has a magnification of +3/25. c) No image is formed in this configuration. d) The image is formed 0.6 cm to the right of the lens and it has a magnification of 3/25. e) The image is formed 1.7 cm to the right of the lens and it has a magnification of 1/3.
Slide 25 Reflection through spherical mirrors : Group Work In pairs: Go back to your notes and fill the table: For thin symmetric lenses (both sides are convex or both are concave): Lens Type Converging Diverging Object Location Inside F Outside F Anywhere Image Sign Location Type Orientation of f of r of m Image on the same side as object? Or opposite side of lens? Image virtual? or real? Image same as object? Or inverted? You will need this info to tackle H.W. and tests Sign: give the sign of the quantity ( + ) or ( - )? Fill in (+/-) if the sign is ambiguous.
Slide 26 Homework : Q1:
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Slide 33 Homework : Q7: Optional
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Slide 35 (last) Summary: Refraction through thin lenses: 1. Refraction through single spherical refracting surfaces. 2. Lenses: converging and diverging. 3. Lenses: thin and thick. 4. Refraction through thin spherical lenses. 5. Lateral Magnification. Next lesson will cover: Thin lens combinations + Refraction through thick lenses + Optical Instruments (maybe) Any Questions?