LAST REVIEW (Covers to the End of the Semester)

Transcription

1 Physics 2020 Suggested for final. There is no final review. LAST REVIEW (Covers to the End of the Semester) 1. A metal rod slides at a constant velocity v over frictionless rails separated by a distance as shown at the right. A uniform magnetic field B is directed into the page. The rod has a resistance R, while the resistance of the rails is negligible. The answers to parts A, B and C are functions of the parameters given in the problem. A. What is the EMF induced in the loop? B. What is the current flowing in the loop? C. What force must act on the loop to maintain the constant velocity v? D. Show that the power put into the system by the external force of part C is equal to the electrical power dissipation. 2. A flat circular coil of 100 turns and radius 10.0 cm (see figure) is located in a uniform magnetic field of T that passes through the coil at The resistance of the coil is An ammeter (not shown) is connected between the point A and B. A. Determine the flux of the magnetic field through the circular coil. B. Under the above conditions, what is the ammeter reading? C. Suppose the magnetic field is now increased from T to T in 0.00 s without changing its direction. After the 0.00 s the magnetic field stays at T. What is the ammeter reading (1) during the 0.00 s interval?. A 00 turn solenoid with a length of 20.0 cm and a radius of 1.50 cm carries a current of 2.0 Amps. A second coil of 4 turns is wrapped tightly about this solenoid such that it can be considered to have the same radius as the solenoid. A. Find the magnetic flux through the second coil. B. Find the magnitude of the average induced emf in the coil when the current in the solenoid increases to 5.00 Amps in a period of seconds. 4. The following diagrams are two views of a rectangular coil ( = 12.0 cm, w = 8.00 cm) of N = 200 wraps. The coil sits in a field that makes an angle of = 0.0 with respect to the plane of the coil. The resistance of this coil is is out of the plane of the paper. Edge View View Looking Down Field Lines

2 For the first 10.0 s the field is a constant 6.00 T. Between t = 10.0 s and t = 22.0 s the field decreases uniformly to zero. See plot. A. What is the magnetic flux passing through the coil for t 10.0 s? B. What is the magnitude of the induced emf in the coil for t 10.0 s? C. What is the magnitude of the induced emf in the coil for 10.0 s t 22.0 s? D. What are the current I and the direction of current flow in the coil during 10.0 t 22.0 s? You may show the current direction as an arrow in the right coil view. Assume you observe the coil from above. 5. A. A 2.4 cm tall object is placed 15.0 cm in front of a convex mirror (R = 20.0 cm). See figure. Using a straight edge, construct a ray diagram showing the image formed by the mirror. Characterize the image. B. The same object is placed 20.0 cm in front of a convex lens. The image formed is inverted and is three times the size of the object. What is the focal length of the lens and where is the image formed? C. What would be the answer to part B if you were told the image was erect, but still three times as large as the object? 6. A ray of light is incident on the vertical face of a right triangular glass prism (see figure). The angle of incidence is 15 and n = 1.6. What is the angle between the ray exiting the prism and the normal to the face of the prism from which the ray exits? Note: The exiting ray is not shown. You must figure out the face the ray exits and draw the complete path. 7. For this problem you need the following data: 6 Radius of the moon: r m = m Distance to the moon: d m = m Focal length of the concave objective mirror at Mt. Palomar: f = 16.8 m A. Determine the radius of curvature of the mirror. B. Construct a simplified ray diagram showing the moon, the mirror, and the moon's image. Draw a ray from the top edge of the moon though the center of curvature of the mirror reflecting back through the image. C. Calculate the position of the moon's image. D. Determine the radius of the moon's image. E. Is the image inverted or not? In all of this, ignore any eyepiece or additional mirrors. It will probably be inconvenient to try to draw the system to scale.

3 8. A. Plane electromagnetic waves are traveling from the left and arrive at a glass interface. The incidence is normal. Draw a collection of wavefronts in the air and another collection in the glass. AIR GLASS Interface B. Construct ray tracing diagrams (use only 2 rays in your construction) to locate the images of the objects shown. Then characterize each image (a) (b) (c) 2. (a) (b) (c). (a) (b) (c) 4. (a) (b) (c) C. Unpolarized light of intensity S o is incident from the left on a series of poalrizers. The angle between the transmission axes of P 1 and P 2 is In terms of S o, the average intensities at A and B are: 2. A third polarizer P is placed first at A then at B. (a) What must be the angle between the transmission axes of P 1 and P so that no light reaches P 2 when P is placed at A? (b) What must be the angle between the transmission axes of P 1 and P so that no light emerges to the right of P when P is placed at B?

4 9. A 8.10 cm tall candle is placed 48.0 cm to the left of a spherical mirror. A real 2.70 cm tall image is formed. A. Is the mirror concave or convex? B. What is the focal length of the mirror? C. Where is the image located? D. Construct the ray diagram. 10. A nearsighted person wears glasses to correct for a far point that is m away from the eye. Neglect the distance of the glasses to the eye. A. What are (i) the focal length and (ii) the power in diopters that will allow this person to see objects clearly. B. Suppose the nearsighted person is able to read a book without his glasses at a distance of 25.0 cm. With the glasses, how close to the eye can the book be brought? C. Suppose as a result of wearing these glasses, the person's near point is actually moved to 75.0 cm from the eye. This is the reason bifocal glasses are made. What is the power in diopters of the second bifocal surface that must be constructed in the same pair of glasses to allow this person to return the book to 25.0 cm? 11. A ray of light is incident normally upon a prism as shown. The index of refraction of the prism material is The prism faces are identified as a, b and c. A. Draw the path of the ray as it passes through the prism and emerges from face c. Neglect the part of the ray that reflects off face c. B. What is the angle of incidence of the ray on face c? C. By what angle does the ray that emerges from face c deviate from the direction of the original ray? D. The incident ray is now tilted upward from the horizontal at a certain angle of incidence,, until the refracted ray in the prism strikes face c at the critical angle of incidence for the prism. What is that critical angle and what is the angle for the original incident ray? 12. A make-up/shaving mirror is designed to magnify the user's face by a factor of 1.2 when the face is placed 20.0 cm in front of it. A. Is the reflection surface convex, concave, or plane? B. Characterize the image. C. What is the radius of curvature of the mirror? D. In the space below construct a ray tracing diagram for the situation described. Use an arrow to represent the face and locate the mirror so its center is at the spot on the line. 1. A lady needing corrective eyeglasses has a near point of 1.50 m. This person performs the following little experiment. With her eyeglasses she forms the image of a ceiling fixture in her living room The fixture is a distance of 1.42 m above the glasses and the image forms on a table 0.8 m below the glasses. A. Is this lady nearsighted or farsighted? B. What is the focal length of the eyeglass lens and what is its power in diopters. C. With the glasses on, how far in front of the glasses should an object be placed so that the woman can see it clearly?

5 14. A. Two students, Delrod and Charlene both wear corrective lenses. One is nearsighted and one is farsighted. Delrod's glasses will form a real image of a distant object on a nearby piece of paper while Charlene's glasses cannot from a real image no matter where the object is placed. For the following, enter Delrod, Charlene, both, neither, or cannot tell. 1. is the nearsighted student. 2. is the farsighted student.. is the student whose far point is within a few meters of the eyes without the glasses. 4. is the student whose near point is far beyond 25.0 cm from the eyes without the glasses. 5. is the student whose glasses form a virtual image beyond 25.0 cm. B. Monochromatic light is incident upon a single slit of width W. A diffraction pattern is viewed on a screen a distance L from the slit. The following asks you to indicate whether the width of the central maximum of the diffraction pattern increases, decreases, or remains the same size. 1. when W is increased. 2. when L is increased.. when is reduced. 4. when the length of the slit is made longer. 5. when the light is made brighter. 15. A 10.0 cm tall candle is placed 40.0 cm in front of a concave mirror of radius R = 60.0 cm. See figure. A. Determine the position and size of the image of the candle formed by the mirror. B. Characterize the this image and draw a ray diagram on the figure. C. A second mirror (concave) whose radius is R = 60.0 cm is placed 10.0 cm to the left of the candle. The convex surface is the surface facing the candle. 1. Determine the position and size of the image of the candle formed by those rays coming directly from the candle to the convex mirror. 2. Characterize this image. D. Determine the position and size of the image of the candle formed by the convex mirror coming from the rays reflected from the concave mirror. 16. A ray of light ( = 60 nm) is incident horizontally on a prism as shown. Take n = A. Complete the ray diagram showing the refraction into the prism and the refraction exiting the prism from its right force. B. What is the initial angle of incidence? C. What is the first angle of refraction? D. What are (i) the second angle of incidence and (ii) the second angle of refraction? 17. An object in the shape of an arrow (h o = 2.0 cm) is placed 12.0 cm in front of a converging lens of focal length f = 4.00 cm. See figure. A. Find analytically the location of the image and characterize the image completely. B. How tall is the image? C. Use the above figure and do the ray tracing to find the image. D. Place a screen at the image location for part A. Assume the lens can be moved along the principle axis between the original object and the screen. There is an additional position of the lens for which a distinct image will form on the screen. Where is it?

6 18. A spherical mirror is used to form an image 5 times the size of an object on a screen located 5.00 m form the object. A. Is the mirror convex or concave? B. Where should the mirror be placed relative to the object? C. What is the focal length of this mirror? D. Construct a ray diagram for this arrangement. You must do all of the drawing. E. Describe what happens to the image if the object is moved 0.50 m closer to the mirror. 19. A not very bright electrical engineer designs a radio transmission-receiving system between two buildings as shown. The distance between the buildings is d = 200 m and the building is h = 60.0 m. For the wavelength chosen the reception at the receiving antenna is terrible, almost nonexistent. The ground between the antennas is flat and smooth. A. Provide a qualitative explanation for why the reception at the receiving antenna is so poor. B. What is the longest wavelength for which the reception is terrible? Note: The fact that the ground between the buildings is flat and smooth is important. C. What would the electrical engineer do to the transmission signal to improve its reception dramatically? 20. A. Monochromatic light arrives at the surface of a fresh water pond on which sits an oil film of thickness t at near normal incidence. See figure. At a wavelength of 400 nm the bird sees the reflected light as enhanced in brightness and at a wavelength of 600 nm the fish sees the transmitted light as enhanced. 1. What is the minimum non-zero thickness of the oil film? 2. Are there any other visible wavelengths seen as enhanced in brightness by the bird or fish? Justify your answer. B. Coherent light is incident upon a screen containing two long narrow slits mm apart. An interference pattern is cast upon a viewing screen 2.00 m away. On the viewing screen, what is the distance separating the first order fringe of the violet light ( = 400 nm) from the second order fringe of the red color ( = 600 nm)? The order of a fringe refers to the fringe beyond the central fringe in the pattern. 21. Two perfectly flat plates of glass are separated by an air film of thickness t. When the plates are illuminated at practically normal incidence by either violet light ( = 450 nm) or yellow light ( =600 nm), an observer looking from above the upper plate sees nothing. See figure (n = 1.00, n = 1.68) air glass A. Draw a ray diagram on the figure that displays the interference situation. That is, on the figure show the rays responsible for the interference effect detected by the observer. B. Determine the minimum thickness of the air film, t. C. Suppose the observer now moves to a position directly below the bottom plate and observer. Does she still observe no transmitted light due to interference? Explain.

7 22. A. When 2 pieces of glass form a wedge as shown, an observer viewing at near normal incidence sees an interference pattern. What kind of fringe (bright or dark) does the observer see when looking at the edge where the plates are in contact? Account for this. B. When coherent monochromatic plane waves arrive at a narrow slit parallel to the slit, a diffraction pattern appears on a screen. Describe how the Huygen's technique accounts for the first minimum in the pattern. C. Explain the term coherent. D. Why are there missing maxima in a 2-slit interference experiment? 2. A. A scuba diver is investigating an oil spill in the ocean. He is trying to determine the thickness of the oil film laying on the sea water. Take n oil = 1.52, n air = 1.00, and n sea water = 1.4. See figure. The diver shines light from a monochromatic source. Yellow-green light ( = 50 nm) is used, and the diver notices that at this wavelength he sees nothing in reflection. Determine the thickness t of the film. You may assume this is the smallest thickness possible for the conditions of the problems B. Two stars in a binary system 120 light year (LY) distant are separated by 1 AU. An Au is an astronomical unit = m. Note: 1 LY = m. What is the maximum wavelength that should be used for the Hubble telescope (D =.00 m) to see these stars as distinct objects according to the Rayleigh criterion. 24. In a double slit experiment coherent light of wavelength 640 nm illuminates the 2-slit arrangement. A second color 2 also illuminates the 2-slit arrangement. On a screen 2.25 m away the location of the second maximum beyond the central maximum for the 640 nm light is the same place as that for the rd minimum beyond the central maximum of the light of wavelength. The slit separation is 0.60 mm. 2 A. What is the actual location y at which the 2nd maximum for the 640 nm light overlaps the rd minimum of the 2 light? B. What is the value of 2? C. Suppose the width of each slit opening is mm. Where is the location of the first missing maximum in the 2-slit display for the 640 nm light? D. How many 2-slit bright fringes fall inside the central maximum of the diffraction pattern for the 640 nm light? 25. A thick plate of flint glass (n = 1.66) rests on top of a thick plate of transparent acrylic (n = 1.50). A beam of light is incident on the top surface of the flint glass at an angle of incidence i. The beam passes through the glass and the acrylic at an angle of 40 with respect to the normal. A. Sketch the physical setup showing the complete light path of the incident beam through the pair of plates. B. Determine the value of. i 26. In a Young's 2-slit experiment (d = 0.20 mm) coherent light from 2 sources, 1 = 450 nm and 2 = 600 nm illuminate the double slit (see figure). There is a point P on the screen, a distance y up from the center line at which a maximum from 1 overlaps a minimum from 2. This point P is the closest such point to the center line for the described overlapping. A. What is the position y at which this overlapping occurs? B. Counting the central bright fringe as the first bright fringe (0th order bright fringe) and the first dark fringe above the center line (0th order dark fringe) as the first dark fringe, then at the position P which bright fringe is overlapping which dark fringe?

8 27. A m foot stool is placed in front of a lens. On a screen 4.00 m away from the stool is displayed the stool's image. The image of the stool is.00 m tall on the screen. A. Is the lens used a positive or negative lens? Characterize the image formed on the screen. B. Determine (1) s o, (2) s i, and () f for this lens. C. Construct a ray tracing diagram for the situation. For simplicity represent the stool as shown. You will have to add the lens. D. Suppose the lens is now slowly moved away from the stool toward the screen along the line of its original axis. Describe what happens to what you observe on the screen. You may assume the lens stops moving when it is a few centimeters from the screen. 28. A woman who is 1.72 m tall stands 2.00 m from the left edge of a diving pool that is 4.60 m deep and 15.0 m across. See figure. ( = 1.) Assume the woman's eyes are 6 cm below the top of her head. Note: Angles are too large for small angle approximation. A. What length L across the bottom of the pool, measured from the left edge is the woman unable to see when she peers at the pool's bottom over the left edge? B. If the woman were to tell you the depth of the pool (apparent) as she reckons it, what value would she give? You may use the small angle result here. C. Suppose this woman cannot see any object beyond m clearly. Objects closer than this distance are clearly seen and objects farther away are blurred; so the woman does not see the bottom of the pool clearly. 1. Is the woman farsighted or nearsighted? 2. What must be the corrective power (in diopters) of the contacts (lenses) she must wear to see the bottom of the pool clearly? Remember the corrective lens the woman wears should allow her to see things infinitely far away at her previous far point. 29. A. Unpolarized light is incident from the left upon a polarizer as shown. The average intensity of the incident light is. The direction of the transmission axis of the first polarizer is shown. Take that direction to be "vertical in the paper. 1. What is the average intensity of the polarized light at A after passing through this first polarizer? 2. A second polarizer (see figure) is placed to the right of the first polarizer. What is the smallest acute angle between the direction of the transmission axes of the two polarizers for the average intensity of the light at position B to be 1/8 of the original average intensity of the light before passing through the first polarizer?. Suppose a third polarizer is inserted at position A in the figure above. How could the direction of the transmission axis of this third polarizer be oriented so that no light is seen at location B?

9 B. 1. Carefully construct a ray tracing diagram to show the image formed by the optical device of the object shown. 2. In the space below characterize each image. (a) (b) (c) Lens Mirror. Somewhere in the above diagrams, mark a place where a human observer could be placed to see each image. 0. A. In each of the following situations an item of interest (loop, coil, bar) is experiencing a changing magnetic flux. In cases a, b, c, d and e indicate the direction CLEARLY of the induced current flowing through R. In the last case, f, indicate the direction of B. a b c d e f Switch S is just closed I in wire below loop is Switch is just closed Arrows in moving bar show direction of decreasing induced there. Indicate direction of through which bar is moving B. Show that the units of are m/s.

10 1. A circuit in the shape of a square 4.00 cm on a side has a resistor in one of its sides. This circuit sits inside a solenoid with a circular cross section (radius 10.0 cm) that is 25.0 cm long and is wound with 500 wraps of wire. See figure. At the initial instant a steady current of 5.00 A flows through each wrap around the solenoid. A plot of the current vs. time is also shown. View is along axis of solenoid A. What is the direction of the induced current through R during (1) the first 2.0 milliseconds; (2) the - next 4.0 milliseconds. [Note: 1 ms = s] B. What is the value of the magnetic flux in the square circuit at t = 2.0 ms? C. What is the induced emf across the resistor in the square circuit between t = 2.0 ms and t = 6.0 ms? D. What induced current is flowing through R at t = 4.0 ms? 2. A. The picture below shows a circular coil of wire with a radius of 15.0 cm having N = 120 turns. The ends of the coil are connected to a 2.40 resistor that is now shown. The coil sits in a uniform magnetic field of =.20 T making an angle of 7 with respect to the normal to the plane of the coil. (a) (b) 1. What is the flux B of the magnetic field through a single t urn of the coil. 2. Suppose now someone grabbed the coil at points L and R and pulled in such a way that the circular shape was pulled to a straight line. This pulling was done in such a way that the decrease in the area of the coil was at a constant rate and took s to fully flatten the coil leaving zero area. What induced emf,, would appear across the ends of the coil while it was being flattened. Assume the angle between and the normal to the plane of the loop does not change while L and R are being pulled apart.. On drawing (b), show the direction of the induced current. 4. Assuming all the resistance of the coil-resistor arrangement is in the 24.0 resistor, what induced current flows through the resistor while the coil is being flattened? B. The picture below shows unpolarized light incident from the left upon a pair of polarizers. The 2 intensity of the unpolarized light is 15.0 W/m. The vertical dashed line in the left polarizer shows its transmission axis (TA). 1. What is the intensity of the light as it passes point A? 2. After passing point A, the light now passes through a second polarizer, and then passes 2 point B. At B the light s intensity is.0 W/m. What is the smallest angle between the directions of the TA s of the two polarizers?

11 . A. A concave mirror is used to project images from a 16.0 mm film onto a screen a distance of 0.0 m from the mirror. The 16.0 mm refers to the height of each film frame. The images displayed on the screen fill the entire 1.60 m height of the screen. 1. What is the focal length of the concave mirror? 2. Now, the film is moved 10.0 cm closer to the mirror. Give a complete characterization of the image the mirror now forms. B. Three polarizers are shown in the drawing. Unpolarized light of intensity S is incident from the left. The angles 1, 2, and are all measured relative to the vertical which is shown in the drawing. In the table below express the intensity of the light in the given region in terms of S according to the values of the angles 1, 2, and. Use the back of the paper for calculations. Intensity 1 = 0 2 = 45 = 45 1 = 15 2 = 15 = 60 1 = 0 2 = 90 = 0 1 = 0 2 = 0 = 90 1 = 0 2 = 0 = 90 Between 1 and 2 S/2 Between 2 and To the right of 4. A. In each of the following situations an item of interest (loop, coil, bar) is experiencing a changing magnetic flux. For each case show the direction of the current induced to flow through R. (a) magnet if falling along axis of loop. (b) magnet if moving to the left away from the circuit (c) the current in the wire above the loop is increasing. (d) the switch S is just closed. (e) In the picture to the right a bar of metal is moving in direction shown. The arrow inside the metal bar shows the direction of an electric field set up inside the bar due to the motion of the bar through a of.. Next to the bar indicate the direction B. The figure to the right shows a collection of polarizers. For simplicity take 1 = 0.0, ie., the transmission axis of the initial polarizer is along the vertical. Points A, B and C are along the axis of the collection. Assume light incident from the left is unpolarized and has a intensity S. 1. The intensity of the light at A no matter what 1 is. o

12 2. Assuming 1 = 0.0 the value 2 must be so that S (at B) equals S (at A)?. Assuming 1 = 0.0 the value 2 must hae so that S (at B) = Assuming 1 = 0.0 and = 90, what must the value of 2 be so that no light reaches point C? 5. Assuming 1 = 0.0 and 2 = 0, what is the value of, reckoned from the vertical as shown in th epicture, for which S (at c) = 0? C. You (the object) are standing in front of a concave mirror. You move to the various points indicated by A, B, C, D and E as shown in the drawing. Note: Point B is at the center of curvature of the mirror. 1. Locations(s) of object where image is/are real. 2. Location of object where image is the same size as the object.. Location of object where image in inverted and smaller than object. 4. Location of object where the real image is farther from the mirror than you. 5. Location of object where you see an erect image. 5. A coil of wire of 120 wraps in the shape of a rectangle (a = 0.80 m) sits on a table. A magnetic field passes through this coil making an angle of = 5.0 with respect to the plane of the coil. See figure. Suppose the magnitude of varies as shown on the graph to the right. A. What is the flux of the magnetic field through the coil during the first.00 s? B. What emf is induced int eh coil during the first.00 s? C. What emf is induced in the coil during the last 2.00 s? D. If the coil forms a closed circuit whose resistance is R = 225, what induced current flows through the coil during the last 2.00 s? E. On the diagram showing the coil sitting on the table, draw the direction of current flow in the coil during the last 2.00 s. 6. A concave make-up mirror produced an erect image athat is 2.50 times the size of the object when the object is placed 12.0 cm in front of the mirror. A. Determine the focal length of the mirror. B. Determine the image distance for this setup. C. Use an arrow for the object and construct a ray tracing for the situation above.

13 7. A. In each of the following situations an item of interest (loop, coil, bar) is experiencing a changing magnetic flux. For each case show the direction of the current induced to flow through R. (a) magnet if rising along axis of loop. (b) magnet if moving to the right(c) the current in the wire to the toward the circuit right of the loop is increasing. (d) just after S is opened. (e) In the picture to the right a bar of metal is moving in direction shown. The arrow inside the metal bar shows the direction of an electric field set up inside the bar due to the motion of the bar through a. Next to the bar indicate the direction of. B. The figure to the right shows a collection of polarizers. For simplicity take 1 = 0.0, i.e., the transmission axis of the initial polarizer is along the vertical. Points A, B and C are along the axis of the collection. Assume light incident from the left is unpolarized and has a intensity S o. Note that all the angles, 1, 2, and are measured relative to the same vertical. In the following table based upon the values of 1, 2, and given at the top of the table, enter the intensity of the light at the indicated location in terms of S. Note: o Intensity 1 = 0 2 = 45 = 45 1 = 0 2 = 60 = 60 1 = 0 2 = 90 = 0 1 = 0 2 = 0 = 90 1 = 0 2 = 0 = 90 At A S o/2 At B At C Look at the last column with angles 1 = 0, 2 = 0 and = 90. What would be the intensity at C in terms of S if the middle polarizer were removed? 2

14 8. A tightly-wrapped circular coil of radius r = m with 100 turns (wraps) of wire, is sitting on a table. The ends of the wire are attached to a small light bulb whose filament has a resistance of R = 75. A magnetic field, which the entire coil feels, is then turned on. The field makes an angle of 7.0 with respect to the normal to the coil and its magnitude changes according to the following graph. A. What is the flux of the magnetic field through a single wrap of the coil at the instant t = s? B. What is the time rate of change of the flux through the entire coil from t = s to s? C. What is the induced emf during the period from t = s to t = s? D. What induced current flows through the filament of the light bulb during the interval from t = s to t = s? E. Looking at the coil from above the table, is the current flow through the coil clockwise (CW), or counterclockwise (CCW)? F. From the time t = s to t = s, what induced emf is developed across the ends of the filament? 9. A. The image formed by a convex mirror (R = 70.0 cm) is located 6.00 cm from the mirror. 1. What is the image distance? 2. What is the object distance?. If the height of the image if 4.80 cm, what is the height of the object? 4. Characterize the image. B. 1. You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking our view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird s image? 2. On the drawing locate the image of the bird formed by the plane mirror the camera is photographing. Do this by carefully tracing a pair of rays that show where the image forms.