Reflection, Refraction and Lenses Geometric Optics Reflection, Refraction and Lenses  

Refraction in Lenses OBJECTIVES Understand how light is refracted and transmitted through lenses to form images. Know the difference between concave and convex lenses? Master the skill of constructing ray diagrams of objects in front of lenses to predict where an image will be and what it will look like. Start out plane mirrors Follow law of reflection sll parallel beams strike surface and surface is uniform so all normal to surface are uniform so they all pont off in same direction. Come in parallel and so leave parallel. Since leave parallel they never go through a focal point. So they never have a chance to flip upside down or invert. That is not true with all mirrors, only true of flat mirrors

Lenses Lens is a piece of transparent material, such as glass or plastic, that is used to focus light and form an image. Convex Concave

Convex Lenses F Convex lens is thicker at the center than at the edges Convergent lenses because they refract parallel light rays so that the rays meet at a point – focal point. Rays from distant objects are parallel So focal point can be found by locating point where the suns rays are brought to a sharp image F

Concave Lenses Lenses are thinner in the middle than around the edges. Divergent lenses because when surrounded by material with a lower index of refraction, rays passing through it spread out. The focal point is the point from which the diverging rays seem to emerge F

Convex Lens Optical axis R R f f Principal axis C F A F C C: Center of curvature R: Radius of curvature (2f) F: Focal Point f: focal length A: vertex, center of lens

Lens C x x x x x C F A F Object Going to look at curved mirrors, specifically curved mirrors with a spherical shape (spherical mirrors) Principal axis connects center of mirror, A, to center of curvature C is center of curvature F is Focal point A is the vertex The image location of an object in front of a lens is the location where all its light intersects after refracting and passing through the lens. The image is the intersection point of all refracted rays.

Ray tracing To find the image of an object, we will trace a few rays through the lens and see where they intersect. The intersection of rays after passing through the lens locates the image of the object Ray tracing is a method of constructing an image using the model of light as a ray. We use ray tracing to construct optical images produced by mirrors and lenses Ray tracing lets us describe what happens to the light as it interacts with a medium Once f is known image position can be found for any object. To find the image point by drawing rays would be difficult if we had to determine refractive angles by Snells law for all the rays. Instead we can make use of certain facts we already know like a ray parallel to the axis of lens passes thru focal point after passing thru lens. In fact, to find image point, we only need 3 rays. These rays, emanating from single point on the object are drawn as in the lens is infinitely thin and we show only a single sharp bend in the lens instead of refractions at each surface.

Ray Diagram-Convex lens Principal ray Central ray C C Image x x x x x F A F Object Focal ray This Image is Located opposite side, beyond C Real Inverted and Enlarged in size Focal point on each side of lens Principal ray - Parallel – so converges to real focus Central – directed to center of lens where the 2 surfaces are essentially parallel to ea other. The ray therefore emerges at same angle it entered. Would be slightly displaced but we assume the lens is very thin. Focal - Headed for virtual focus – therefore muxt be parallel on other sideparallel Actually 2 rays are sufficient but we use a 3rd to check Thiis finds image on other side of the lens for one point on object. Can do for all the other object points to find the complete image Because the light rays actually pass thru the image, it could be detected by film or seen on a wheite pice of paper - Real image – paper can be ignited by producing a REAL image of the sun on paper Image of top of object

Ray tracing To find the image of an object, use the following principal rays the p-ray, which travels parallel to the principal axis, then refracts through the focal point. The f-ray, which travels through the focal point, then refracts parallel to the principal axis. The c-ray, which travels through the center of the lens and continues without bending.

Ray Diagram-Concave lens Principal ray Focal ray Object f Image f Central ray This Image is Located same side, inside f Virtual (on same side) Upright and Reduced in size

Optical Image Location Size Type Orientation upright inverted True Enlarged Reduced Type real (converging rays) virtual (diverging rays)

CONVEX Lens IMAGE CONCAVE Lens IMAGE OBJECT Location CONVEX Lens IMAGE Location Orientation Size Type Beyond C Between C and F Other side inverted Reduced real At C Other Side Inverted True Enlarged At F NO IMAGE Inside F Same Side Upright Virtual OBJECT Location CONCAVE Lens IMAGE Location Orientation Size Type Very far away Inside F Same Side Upright Reduced Virtual Very close

The Lens Equation do di ho f Image Object f hi

Thin Lens Equation f is positive for convex, converging lenses The thin lens equation relates the focal length of a spherical thin lens to the object position and the image position f is positive for convex, converging lenses f is negative for concave, diverging lenses di is positive for real images di is negative for virtual images

Lateral Magnification hi is positive for upright images hi is negative for inverted images

Example: Image formed by converging lens Example: Image formed by converging lens. What is a) the position and b) the size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal length camera lens? f f a) Image is behind lens, only 2.6 mm farther from the lens than would be the image for an object at infinity.

Example: Image formed by converging lens Example: Image formed by converging lens. What is a) the position and b) the size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal length camera lens? f f b) Image is 4 mm high and inverted (m<0)

Example: Object close to a converging lens Example: Object close to a converging lens. An object is placed 10 cm from a 15 cm focal length converging lens. Determine the image position and size (a) analytically and (b) using a ray diagram f f a) since di<0, image is virtual and on same side of the lens. Since m>0, image is upright

Example: Object close to a converging lens Example: Object close to a converging lens. An object is placed 10 cm from a 15 cm focal length converging lens. Determine the image position and size (a) analytically and (b) using a ray diagram b) f f Image is virtual and upright

Example: Diverging lens Example: Diverging lens. Where must a small insect be placed if a 25 cm diverging lens is to form a virtual image 20 cm in front of the lens? f f

DO NOW An object is located 139 DO NOW An object is located 139.0 mm from a 50 mm focal length converging lens. Find the image distance and magnification a) by using a ray diagram b) by calculation a) f f Image is real, inverted and reduced

DO NOW An object is located 139 DO NOW An object is located 139.0 mm from a 50 mm focal length converging lens. Find the image distance and magnification a) by using a ray diagram b) by calculation f b) Image is real, inverted and reduced

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Lenses

DO NOW An object 31. 5 cm in front of a certain lens is imaged 8 DO NOW An object 31.5 cm in front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this and what is its focal length? Is the image real or virtual? Confirm with ray diagram. a) f f Lens is diverging

Chromatic Aberration Light that passes through a lens is ringed with color This results from dispersion of light by the lens Always present when a single lens is used Can be corrected by using two lenses

Our Eyes & Lenses Light that is emitted or reflected off an object travels into the eye through the cornea. The light then passes through the lens and focuses onto the retina that is at the back of the eye. Specialized cells on the retina absorb this light and send information about the image along the optic nerve to the brain.

Focusing Images Light entering the eye is mostly focused by the cornea because the air-cornea surface has the greatest difference in indices of refraction (cornea n=1.376). The lens is responsible for the fine focus that allows you to clearly see both distant and nearby objects.

Accommodation Muscles surrounding the lens can contract or relax, thereby changing the shape of the lens. This, in turn, changes the focal length of the eye. When the muscles are relaxed, the image of distant objects is focused on the retina. When the muscles contract, the focal length is shortened, and this allows images of closer objects to be focused on the retina. Distant vision Close vision

Nearsightedness Focal length of the eye is too short to focus light on the retina. Also known as myopia Objects far away are blurry Fixed with concave lenses

Farsightedness Focal length of the eye is too long and places image past the retina Also known as hyperopia Objects nearby are blurry Fixed with convex lenses Hyperopia. Eye cannot focus on near objects

Camera

Example: An 80 mm focal length lens is used to focus an image on the film/sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 120mm. A) how far ahead of the film should the lens be if the object to be photographed is 3.0 m away?? B) What is the closest object this lens could photograph? f a)

Example: An 80 mm focal length lens is used to focus an image on the film/sensor of a camera. Maximum distance allowed between the lens and the sensor plane is 120mm. B) What is the closest object this lens could photograph? f b)

Refracting Telescope Lenses magnify distant objects Light from stars and galaxies so far away that light is parallel and makes a real image Lens closest to object – objective lens, focuses distant object at focal plane Eyepice acts lime magnifying glass For an astronomical telescope to produce bright images of distant stars, objective lens must be large to allow as much ligh as possible. Indeed diameter of objective is most important parameter which is why largest ones are specified by gining obj diameter The construction and grinding of such large lenses is VERY difficult. Therefore largest telescopes are reflectin telesco[es that use a curved mirrob as objective. SINCE mirror only has one surface to be ground and can be supported along its entire surface(a large lens, supported at its edges, would sag under own weight. Objective lens Eyepiece

Binoculars Lenses produce magnified images of faraway objects Just as separation of your eyes gives a sense of 3D and depth, the prisms allow greater separations of the objectives, thereby improving 3-D

Microscope Used to view very small objects