Solution and Grading Key PHYS1212 / PHYS1252 Quiz #1.04 Ray Diagrams

Transcription

1 (A) Solution and Grading Key PHYS1212 / PHYS1252 Quiz #1.04 Ray Diagrams Only the object is shown here. The image is hidden and you have to infer its location and orientation from the rays as drawn. Red rays are emerging from the object. Blue rays are either refracted rays (if it s a lens) or reflected rays (if it s a mirror). This picture shows the ray diagram of (1) a convergent lens forming a real, erect image to the right of the lens (2) a divergent mirror forming a virtual, erect image to the right of the mirror (3) a convergent mirror forming a virtual, erect image to the right of the mirror (4) a divergent lens forming a real, erect image to the right of the lens (5) a convergent lens forming a virtual, erect image to the left of the lens (6) a convergent mirror forming a virtual, erect image to the left of the mirror (7) a divergent mirror forming a virtual, erect image to the left of the mirror Hints: (a) Inspect the direction of the F-ray and the P-ray in the drawing to figure out where the incoming side of the device is and mark it In. (b) Inspect the F-ray and the P -ray in the drawing to find and mark the focal points F and F on the optical axis. (c) From the location of F and F, figure out if it s a lens or a mirror. From that and from the result of (a), figure out where the outgoing side is and mark it Out. (d) Use the sign convention for F and F to figure out whether the device is convergent ( f > 0 ) or divergent ( f < 0 ).

2 Answer: (3) It s a convergent mirror forming a virtual, erect image to the right of the mirror. Solution steps, following the Hints, see Drawing below: 1) The incident F- and P-ray are striking the device from the left à In is to the left of the device. Mark left side as In and opposite (right) side as Not In 2) Find F: The F-ray (or its extension) intersects the optical axis at F à By inspection, F is located on optical axis to the left of the device. Label it F! 2) Find the P -ray: The P -ray intersects principal plane, H, at the same point as the P-ray and the P -ray is not parallel to the optical axis à See drawing below for P -ray label. 3) Find F : The P -ray (or its extension) intersects the optical axis at F à By inspection, F is located on optical axis to the left of the device, at the same location as F. Label it F! 4) Focal points F and F co-incide on the same side (to the left) of the device à The device must be a mirror. 5) For a mirror, In and Out are on the same side à Out is to the left of the mirror. Mark left side as Out and opposite (right) side as Not Out. 6) Focal point F is on In side of mirror à By focal point sign concvention, focal length, f, must be positive: f >0, i.e., it s a convergent mirror. 7) Find : The intersects principal plane, H, at the same point as the F-ray and the F - ray is parallel to the optical axis à See drawing below for label. 8) Image point is located at the intersection of F - and P -ray à By inspection, the image point is to the right of the mirror, above the optical axis. Draw the vertical image arrow from the optical axis to that image point. 9) Image is on the Not Out side of the mirror à Image is virtual. 10) Image arrow points upward, i.e., has same orientation as object à Image is erect. In Out Not In Not Out F F object image H

3 (B) Only the object is shown here. The image is hidden and you have to infer its location and orientation from the rays as drawn. Red rays are emerging from the object. Blue rays are either refracted rays (if it s a lens) or reflected rays (if it s a mirror). This picture shows the ray diagram of (1) a convergent lens forming a virtual, inverted image to the left of the lens (2) a divergent mirror forming a virtual, inverted image to the left of the mirror (3) a convergent mirror forming a virtual, inverted image to the left of the mirror (4) a divergent lens forming a real, inverted image to the right of the lens (5) a convergent lens forming a real, inverted image to the left of the lens (6) a convergent mirror forming a real, inverted image to the right of the mirror (7) a divergent mirror forming a real, inverted image to the right of the mirror Hints: (a) Inspect the direction of the F-ray and the P-ray in the drawing to figure out where the incoming side of the device is and mark it In. (b) Inspect the F-ray and the P -ray in the drawing to find and mark the focal points F and F on the optical axis. (c) From the location of F and F, figure out if it s a lens or a mirror. From that and from the result of (a), figure out where the outgoing side is and mark it Out. (d) Use the sign convention for F and F to figure out whether the device is convergent ( f > 0 ) or divergent ( f < 0 ).

4 Answer: (5) It s a convergent lens forming a real, inverted image to the left of the lens. Solution steps, following the Hints, see Drawing below: 1) The incident F- and P-ray are striking the device from the right à In is to the right of the device. Mark right side as In and opposite (left) side as Not In 2) Find F: The F-ray (or its extension) intersects the optical axis at F à By inspection, F is located on optical axis to the right of the device. Label it F! 2) Find the P -ray: The P -ray intersects principal plane, H, at the same point as the P-ray and the P -ray is not parallel to the optical axis à See drawing below for P -ray label. 3) Find F : The P -ray (or its extension) intersects the optical axis at F à By inspection, F is located on optical axis to the left of the device, at a location opposite from F. Label it F! 4) Focal points F and F are on opposite sides of the device à The device must be a lens. 5) For a lens, In and Out are on opposite sides à Out is to the left of the lens. Mark left side as Out and opposite (right) side as Not Out. 6) Focal point F is on In side of lens à By focal point sign concvention, focal length, f, must be positive: f >0, i.e., it s a convergent lens. 7) Find : The intersects principal plane, H, at the same point as the F-ray and the F - ray is parallel to the optical axis à See drawing below for label. 8) Image point is located at the intersection of F - and P -ray à By inspection, the image point is to the left of the lens, below the optical axis. Draw the vertical image arrow from the optical axis to that image point. 9) Image is on the Out side of the lens à Image is real. 10) Image arrow points downward, i.e., has opposite orientation as object à Image is inverted. Not In Out In Not Out image F F object H.

5 Quiz Grading Key (unless stated otherwise in class): The maximum score you can reach on this quiz is 100 points. Of those 100 points, you can earn 70 points just for attendance, i.e., for handing in a quiz paper with your name written on it, legibly, regardless of your mastery of the quiz material. In addition, your answer for each part [A) and B)] of this quiz is worth 15 points, if correct, up to a maximum total of 2x15=30 points for correct answers. Each part is graded on an all-or-nothing basis: you either get 15 points or 0 points for each part. There is no partial credit within any part.