From Mirrors to Lenses

c f real image

Real Images Rather than a virtual image (which is formed by virtual rays), a real image is formed by real rays! It can only be produced by a concave mirror, and only if the object is further than the focal point. Since the image is formed by actual rays of light in front of the mirror, it can be projected onto a screen. You need to see it to believe it..

Concave Mirror – Object further than c c f The image is real, inverted, and reduced. P-ray F-ray C-ray Color Code

Concave Mirror – Object at c c f The image is real, inverted, and the same size as the object. P-ray F-ray C-ray Color Code

Concave Mirror – Object between c and f c f The image is real, inverted, and enlarged. P-ray F-ray C-ray Color Code

Concave Mirror – Object at focal point c f NO IMAGE IS FORMED!!! P-ray F-ray C-ray Color Code These will never intersect

Concave Mirror – Object closer than f c f The image is virtual, upright, and enlarged. This is why concave mirrors with large focal lengths are used as makeup mirrors! P-ray F-ray C-ray Color Code

Object LocationImage OrientationImage SizeImage Type Beyond cInvertedReducedReal At cInvertedSame as objectReal Between c and fInvertedEnlargedReal At fNo image Closer than fUprightEnlargedVirtual Concave Mirrors: Summary If the object is further than f, the image will be inverted and real. If the object is closer than f, the image will be upright and virtual.

Convex Mirror – Object anywhere c f The image is virtual, upright, and reduced. P-ray F-ray C-ray Color Code

This is why convex mirrors are used for seeing large areas at once! Object LocationImage OrientationImage SizeImage Type AnywhereUprightReducedVirtual Convex Mirrors: Summary

Real vs Virtual Images Real images are formed by actual light rays (not virtual rays). They are able to be seen directly with the human eye, and can also be projected onto a screen! Virtual images are formed by virtual rays. A virtual image is the appearance of light originating from a certain location, although the light never actually did (it was redirected by a mirror or lens to look like it did!) When a virtual image is formed, it can be seen by the human eye. However, it cannot be projected onto a screen!

What is a lens? A lens is a piece of transparent material that is shaped such that the outside is curved on at least one side. There are many types of lenses, and the two that we will concentrate on in this course are convex lenses and concave lenses. Convex lensConcave lens

The types of lenses that we will be learning about are circular in curvature on both sides.

Convex Lens focal point c Incoming rays that are parallel to the principal axis will all pass through the focal point! This type of lens is sometimes called a converging lens.

Focal point depends on n of lens and medium that it is in! Lenses actually have a focal point on both sides. ff

We will be Working with Thin Lenses This means that you don’t need to worry about light refracting as it enters and as it leaves the lens. You only need to know how to use concepts to draw principal rays. It also means that a light ray passing through the center of the lens (at any angle) will pass directly through the lens, undeflected! The thin lens assumption allows us to draw this ray. With thick lenses, a more complex approach is required.

Principal Rays for Lenses! The principal rays used to locate the image formed by a lens are very similar to the ones used with curved mirrors! The concepts are also very similar. Make sure to pay attention to the concepts, as well as the specific rules for each ray.

P-Ray (Parallel Ray) f Emitted by the object, traveling parallel to the principal axis. It is then refracted through the focal point! f

F-Ray (Focal Ray) f Emitted by the object, traveling through the focal point. It is then refracted parallel to the principal axis! f

C-Ray (Center Ray) f Emitted by the object, traveling toward the center of the lens. It passes through undeflected! f

Concave Lens antifocal point Incoming rays that are parallel to the principal axis will diverge directly away from the antifocal point! This type of mirror is sometimes called a diverging lens.

P-Ray: Concave Version f’f’ Emitted by the object, traveling parallel to the principal axis. It is then refracted directly away from the antifocal point! f’f’

F-Ray: Concave Version f’f’ Emitted by the object, toward the antifocal point on the other side of the lens. It is then refracted parallel to the principal axis! f’f’

C-Ray: Concave Version f’f’ Emitted by the object, traveling toward the center of the lens. It passes through undeflected! f’f’

Concave Lens – Object at any location c f The image is virtual, upright, and reduced. P-ray C-ray Color Code f c

Virtual Images in Mirrors vs Lenses For mirrors, a virtual image will always be on opposite side as the object. Convex mirrors always produce virtual images. Rays appear to diverge from behind the mirror. For lenses, a virtual image will always be on the same side as the object. Concave lenses always produce virtual images. Rays appear to diverge from in front of the lens. c fc f f c

This is the same as for a convex mirror! Object LocationImage OrientationImage SizeImage Type AnywhereUprightReducedVirtual Concave Lenses: Summary Converging lenses and converging mirrors have the same image properties. Diverging lenses and diverging mirrors have the same image properties.

Convex Lens – Object further than c c f The image is real, inverted, and reduced. P-ray F-ray C-ray Color Code f c

Real Images in Mirrors vs Lenses c f For mirrors, a real image can only be produced by a concave mirror, and the image is on the same side as the object. c f f c Rays converge in front of the mirror. For lenses, a real image can only be produced by a convex lens, and the image is on the opposite side as the object. Rays converge behind the lens.

Convex Lens – Object at c c f The image is real, inverted, and the same size. P-ray F-ray C-ray Color Code f c

Convex Lens – Object between c and f c f The image is real, inverted, and enlarged. P-ray F-ray C-ray Color Code f c

Convex Lens – Object at f c f No image is formed! P-ray F-ray C-ray Color Code f c

Convex Lens – Object closer than f c f The image is virtual, inverted, and enlarged. P-ray F-ray C-ray Color Code f c

You now have all of the tools necessary to locate an image formed by any curved mirror or lens. Geometric optics is covered on the AP test, so you should go over this again in your AP review book in the next few weeks. Go forth and make me a proud physics teacher :) (and get college credit for this course)

Object LocationImage OrientationImage SizeImage Type Beyond cInvertedReducedReal At cInvertedSame as objectReal Between c and fInvertedEnlargedReal At fNo image Closer than fUprightEnlargedVirtual Convex Lenses: Summary This is the same as for a concave mirror! This is why convex lenses held close to an object make good magnifying glasses!

This is the same as for a convex mirror! Object LocationImage OrientationImage SizeImage Type AnywhereUprightReducedVirtual Concave Lenses: Summary Converging lenses and converging mirrors have the same image properties. Diverging lenses and diverging mirrors have the same image properties.

Enlightening Concept! A large lens is used to focus an image of an object onto a screen. If the left half of the lens is covered with a dark card, which of the following occurs? (A) The left half of the image disappears. (B) The right half of the image disappears. (C) The image becomes blurred. (D) The image becomes dimmer. (E) No image is formed.

Although principal rays help guide us to locate the image, we cannot forget the important fact that each point on the object emits rays in all directions. The lens is completely filled with rays from every point of the object! (The image is also formed by infinite rays from the middle of the object, the bottom of the object, etc.)

So, if we cover half of the lens... The entire image would still exist! However, less light would be forming the image. Therefore the image would be dimmer.

Which three of the glass lenses above, when placed in air, will cause parallel rays of light to converge? (A) I, II, and III (B) I, III, and V (C) l, IV, and V (D) II, III, and IV (E) II, IV, and V

I, III, and V are more convex than concave – they will cause light rays to converge. II and IV are more concave than convex – they will cause light rays to diverge.

Geometric Optics Equation #1 d i is the distance from the image to the mirror or lens d o is the distance from the object to the mirror or lens f is the focal length of the mirror or lens Applies to both mirrors and lenses.

Focal length can be positive or negative! Mirrors and lenses that have a focal point will have a positive focal length. Mirrors and lenses that have an antifocal point will have a negative focal length. Converging lenses and mirrors (concave mirrors and convex lenses) have a positive focal length. Diverging lenses and mirrors (convex mirrors and concave lenses) have a negative focal length.

A Point of Possible Confusion Real images have a positive d i Virtual images have a negative d i If you end up with a negative d i when you do the calculations, it means that a virtual image is produced! This applies to both mirrors and lenses, and you must be consistent!

A postage stamp is placed 30 centimeters to the left of a converging lens of focal length 60 centimeters. Where is the image of the stamp located? (A) 60 cm to the left of the lens (B) 20 cm to the left of the lens (C) 20 cm to the right of the lens (D) 30 cm to the right of the lens (E) 60 cm to the right of the lens Whiteboard Problem Solving I

A concave mirror with a radius of curvature of 1.0 m is used to collect light from a distant star. The distance between the mirror and the image of the star is nearly (A)0.25 m (B) 0.50 m (C) 0.75 m (D) 1.0 m (E) 2.0 m Whiteboard Problem Solving II

Solution! A star is so far away that we can comfortably use the approximation d o = ∞! This gives Since 1/∞ = 0, this results in d i = f

Geometric Optics Equation #2 h i is the height of the image h o is the height of the object A negative image height means that the image is inverted. Memorize both of these equations (don’t forget the negative sign!)

Attack of the Whiteboard f’f’f’f’ 15 cm 5 cm 10 cm Where will the image be located and what will it look like?

d o = 15 cm f = -10 cm d i = -6 cm (Virtual image 6 cm from lens) h o = 5 cm h i = 2 cm (Inverted and reduced image) f’f’f’f’

Deep Whiteboard Thoughts! dodo hoho An object of height h 0 is located at a distance d o from a plane mirror. Using the mathematical models and, determine the location and height of the image formed by the plane mirror! Hint: What is the radius of curvature of a plane mirror?

dodo hoho f plane mirror = ∞ = 0! d i = -d o This means that the mirror will produce a virtual image (negative image distance) that is equidistant from the mirror. Since d i = -d o  -d i / d o = 1 Therefore h i / h o = 1 h i = h o The image is the same height as the object!