PHYSICS InClass by SSL Technologies with S. Lancione Exercise-52 High School Optics InClass by SSL Technologies with S. Lancione Exercise-52 Lenses Part 1 /2

Lenses Convex Concave PART-1 /2 LENSES Whereas mirrors produce images by reflection, lenses produce images by refraction. Depending upon their “thickness”, lenses are classified as “thick” or “thin”. In this course, we will only consider “thin” lenses. In effect, therefore, we disregard the thickness of the lens assuming it to be a line. Convex Concave Click

Lenses PART-1 There are two main types of lenses called convex (also known as converging ) and concave (also known as diverging ). Convex lenses are thicker in the middle than at the edges while concave lenses are thicker at the edges than in the middle. As illustrated below, both convex and concave lenses each have three variations. Click

Lenses PART-1 Convex Lens Concave Lens When representing “thin” lenses in a diagram, it is sometimes more convenient to simply draw an arrow rather than the actual lens. Using this method, an arrow is used to represent the lens as illustrated below. Convex Lens Concave Lens Click

Convex lenses are thicker in the middle and thus converge light rays. REMEMBER Convex lenses are thicker in the middle and thus converge light rays. Concave lenses are thinner in the middle and thus diverge light rays. Click

Lenses PART-1 Just as with concave mirrors, the characteristics of the image formed by a converging lens depend upon the location of the object. There are six "strategic" locations where an object may be placed. For each location, the image will be formed at a different place and with different characteristics. We will illustrate the six different locations and label them as CASE-1 to CASE-6. Case-1: Object at infinity Case-2: Object just beyond 2 F’ Case-3: Object at 2F’ Case-4: Object between 2F’ and F’ Case-5: Object at F’ Case-6: Object within focal length (f) Click

Convex (converging) Lenses CASE-1 : Object at “infinity” Infinity simply means “far away”. CASE-1 : Object at “infinity” No image Object NOTE Since the object is at “infinity”, all rays arrive parallel. No image formed (All rays pass through F) Click

Convex (converging) Lenses CASE-2 : Object just beyond 2F’ NOTE In order to establish an image point, all we need are two intersecting rays. CASE-2 : Object just beyond 2F’ Note-1 A ray that comes parallel is refracted through F. Note-2 A ray that goes through the vertex goes right through. Note-3 A ray that goes through F’ is refracted parallel. Object Image This ray is extra in locating the image. Image is real (formed by refracted rays) Inverted (upside down) Reduced (smaller than object) Located between F and 2F Click

Convex (converging) Lenses CASE-3 : Object at 2F’ Again: In order to establish an image point, all we need are two intersecting rays. CASE-3 : Object at 2F’ Object Image This ray is extra. Image is real (formed by refracted rays) Inverted (upside down) Same size as object Located at 2F Click

Convex (converging) Lenses CASE-4 : Object between 2F’ and F’ Image Image is real (formed by refracted rays) Inverted (upside down) Magnified (larger than object) Located beyond 2F Click

Convex (converging) Lenses CASE-5 : Object at F’ No image is formed (rays refract parallel) Click

Convex (converging) Lenses CASE-6 : Object is within focal length Image Object Image is virtual (formed by extended rays) Upright Magnified Located on same side as object Click

Now let's consider Concave lenses delay

Concave (diverging) Lenses One case only! Image is always virtual Object Image Image is always virtual (formed by a direct ray and an extended ray) Always upright Always reduced Always located on same side as object Click

Lenses PART-1 Be sure to follow the following sign convention when solving problems concerning lenses.  Sign convention: 1- Object distance is always positive. 2- Image distance is positive if the image is on the side of the lens where light emerges (from lens). 3- Image distance is negative if the image is on the side of the lens where the light enters (the lens). 4- The focal length of a convex (converging) lens is positive. 5- The focal length of a concave (diverging) lens is negative. Click

EXERCISES

Question-1 Convex Converging A lens that is thicker in the middle than at the ends is known as: Convex Converging A lens or a lens. Click Click

Question-2 Concave Diverging A lens that is thicker at the ends than in the middle is known as: Concave Diverging A lens or a lens. Click Click

Question-3 Trace the rays that emerge from the following glass mediums: a) b) c) d) Click Click

Question-4 For each case below, draw the appropriate lens that will produce the indicated rays. a) Concave (diverging) b) Convex (converging) Click Click

Question-5 A mirror forms an image by reflection whereas How is the image formed by a mirror different from the image formed by a lens? A mirror forms an image by reflection whereas a lens forms a an image by refraction. Click Click

Image is real, inverted, reduced and located between F and 2F. Question-6 For each convex lens illustrated below, draw the image. a) Image Image is real, inverted, reduced and located between F and 2F. Click Click

Image is real, inverted, same size object and located at 2F. Question-6 For each convex lens illustrated below, draw the image. b) Image Image is real, inverted, same size object and located at 2F. Click Click

Image is real, inverted, magnified and located beyond 2F. Question-6 For each convex lens illustrated below, draw the image. c) Image Image is real, inverted, magnified and located beyond 2F. Click Click

All rays refract parallel, Question-6 For each convex lens illustrated below, draw the image. d) Parallel All rays refract parallel, no image is formed. Click Click

Question-6 For each convex lens illustrated below, draw the image. e) Image is virtual, upright, magnified and located on same side as object. Click Click

Image is virtual, upright, reduced and located on same side as object. Question-7 For each concave lens illustrated below, draw the image. REMEMBER Concave lenses always produce images that are virtual, upright and reduced. Image Image is virtual, upright, reduced and located on same side as object. Click Click

Image is virtual, upright, reduced and located on same side as object. Question-7 For each concave lens illustrated below, draw the image. Image Image is virtual, upright, reduced and located on same side as object. Click Click

Question-8 Real 60 cm - 3 (inverted and 3x larger than object) 21 cm An object that is 7 cm high is placed 20 cm in front of a convex (converging) lens whose focal length is 15 cm. Determine the characteristics of the image: Real Type (real or virtual): _______________ Location: _______________ Magnification: _______________ Height: _______________ 60 cm - 3 (inverted and 3x larger than object) 21 cm Negative sign indicates inversion. Click Click

Note that diverging lenses have a negative focal length. Question-9 An object whose height is 4 cm is placed 50 cm from a concave (diverging) lens. If the focal length of the lens is 30 cm, determine the characteristics of the image: Virtual Type (real or virtual): _______________ Location: _______________ Magnification: _______________ Height: _______________ 18.75 cm 0.375 (upright and smaller than object) 1.5 cm Note that diverging lenses have a negative focal length. Click Click

Question-10 Real 28 cm - 0.04 (inverted and smaller than object) 2 cm An object that is 5 cm high is placed 70 cm in front of a convex (converging) lens whose focal length is 20 cm. Determine the characteristics of the image: Real Type (real or virtual): _______________ Location: _______________ Magnification: _______________ Height: _______________ 28 cm - 0.04 (inverted and smaller than object) 2 cm Negative sign indicates inversion. Click Click

Question-11 A lens produces the following optical effect. Which group of lens produces the above effect? Plano convex D) Double convex C) Plano concave B) Double concave A) Click Click

Question-12 Beams of light rays are traveling through air parallel to the principal axis of four different lenses. The light rays enter the lenses and are refracted. In which diagram are the light rays correctly illustrated? Click Click

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