Tan Express Spot

Tan Express Spot

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A piece of curved glass has a radius of curvature of r = 9.52 m and is used to form Newton's rings, as in Figure 27.14. Not counting the dark spot at the center of the pattern, there are one hundred dark fringes, the last one being at the outer edge of the curved piece of glass. The light being used has a wavelength of 664 nm in vacuum. What is the radius R of the outermost dark ring in the pattern? Hint: Note that r is much greater than R, and you may assume that tan() = for small angles, where must be expressed in radians.

Graph: http://answerboard.cramster.com/physics-topic-5-256499-0.aspx

Each dark fring away from the center represents a path difference of one wavelength between the reflection from the glass and from underlying surface. So the 100th ring has a path 100 wavelengths longer. The path difference is two times the height of the glass above the surface. So, 2 * h = 100 (wavelength). Solve for h. Then note that h is the difference between r and r cos. Solve h = r(1-cos θ) for θ. Finally, R= r sin θ.

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ESCUELA P. 86096 DE CANSHAN HUARAZ que baile tan tierno no?

History Lesson for Girls: a Novel Excerpt

One Day I saw them, our dream horses, and on that day I pulled over to the side of the road and cried. There they were, Appaloosas and roans and bays, and I thought I saw, squinting into the last bit of sunlight, a gray. All the horses moved together, a makeshift herd -- maybe they'd heard my car, or maybe it was a chill, the first winter breeze, almost imperceptible on a summer day. So many years later and now here they were in front of me. The horses trembled, shifted, and then became calm and separated out again, twelve or twenty of them, more than enough for the Alison and Kate Horse Training Company.

She saved me. That's the first thing you should know about Kate. It was the year we moved to Weston, the year my parents went haywire, the year my back started curving out of control as if it were the life of the party. She was five feet seven and had long brown hair bleached by the sun, and her father was an Egyptian emperor. Was he for real? Real enough for a small suburban dynasty. Real enough to pass on a legacy.

I think of Kate all the time. I think of her like I've got this little silver Egyptian cat in my pocket, a little silver talisman that won't go away. I think of her, and then I think of him, too, Tut Hamilton, sham shaman in suburbia. I can't forget him, any more than I can forget her.

The thing is, she saved me that year, and then it was my turn. That's what friendship is. That's how to make history.

I was thirteen when my parents and I moved to the fancy town of Weston from maligned and honorable Norwalk, two towns over. We were ready for anything, ready for the good things to start happening, and the first thing that went wrong was the blue room.

Mom wanted her studio to be blue, despite the fact that most painters prefer a room absent of color, a blank wall, a clean palette. She'd had a vision, you see, a dream of a blue room.

My father offered to paint the room for her, but she would choose the color, of course. She and I went to the paint store together.

"These men -- they're painting the world, creating color wheels, color contrasts, color inspirations -- without any real conception, no awareness at all, of what they're doing. They could be artists -- but no, no -- instead of using these glorious choices -- all the glory, all the opportunity, Alison -- they just sit around drinking coffee out of a thermos and painting houses tan, tan, and tan again. How dreary . . . "

She continued talking as we got out of our Corolla (it also happened to be tan) and walked the short distance from the parking lot to the shopping center. I did hope she'd stop, or at least lower her voice, before we got to the store. She had a way of causing a commotion, despite her size. She was a tiny, fragile person, swathed in scarves and perfumes and charms.

Men of uncertain age and weight looked our way as we came in: Scheherazade and the too tall, too bony, too elbowy stalk, in a back brace, beside her.

My mother breezed by their troubling, huntery expressions, and we settled in before the paint chips. I'd just turned thirteen, my back was curved, and my parents were curved, too -- bohemians in Connecticut, the Land of Plenty. Either all the colors looked good to me or none of them did. Somehow it seemed that this, like everything else, could go either way.

Mom, however, was confident. She hummed with satisfaction, picking out various small, hopeful cards from the rack, cocking her head, pursing her lips -- rejecting one, then the other, until she came to her blue.

Today they've gotten hold of Weston and thrown up these monstrous vault homes, decorated with pillars and neo-this-and-that architectural details, but in 1975 the lovely colonials were what stood out, the historic touch. Some even had plaques near the doorways saying things like Paul Revere Slept Here in 1782 or In 1801, Here Stood Weston's First Mill. The split-levels such as ours, built in the aesthetically challenged sixties, were scattered like tawdry cousins among these statelier, storied homes. Still, moving to 12 Ramble Lane was a big step up for us, and my parents had attached hopes to the house, obvious as the taped-up notes left behind by the house's former owners ("Use 5-watt bulb MAX!" "Filter hose needs to be checked 2X year!"). Mom had torn down their notes impatiently the first day we moved in, replacing them with a sign of her own. Purple felt with silver letters, it hung on the door of her soon-to-be-blue room, her first real studio: "Artist at Work." She could turn it to face in or out, indicating whether she was "open" or "closed" -- a novel idea in a mother. Dad's office was in the basement (he had another at the university), but most of all he seemed keen on a certain green hillock in the backyard, where he could sit cross-legged and rumble with a middle-aged Om.

We were all dressed up now, decked out in zesty Marimekko. And although the first two weeks in Weston passed in a kind of misty, glorious disappointment, most of all we felt lucky to be there, in a town of lilacs and curving roads and studio doors that shut and hillocks and a barn.

Dad stood on the ladder. He'd painted all the edges first, near the ceiling and floors and windows and corners, and then he'd taken out the roller and started in on wide swaths of Prussian Wildflower.

"A bit dark, isn't it?"

"Well, it's what your mother wants. It'll lighten up as it dries, too, Allie Oop."

This cheerfulness was disconcerting. He'd been duped into thinking he could please my mother.

"It looks different from the little card."

"Goddammit," Dad said. A slop of paint had fallen to the floor.

The fact of the matter is, both my parents were fish out of water in Weston. Mom with her dreams of being a painter and Dad with his day job and his poetry books, including the award-winning one, all lined up on the mantel. They were attempting to piece together a life with art at its center and also (not that I was fully aware of this at the time) making choices based on what might be good for me, their daughter. Art geeks, adversaries, people who drove old cars: They weren't part of the PTA crowd, and they weren't swingers, either. Mainly they were simply my parents, and it was extraordinarily embarrassing, but seemed pretty natural, that they were so weird.

"Look, you can't tell anything from the card," he said. "Take a rag to that spot, would you, please?"

"Why do they have the cards, then?"

"To beguile the willing, Alison."

"Why would they do that? They would never do that."

"You don't think so? Think about the visceral and dark depths of the workingman's resentment, darling, and you might have another idea."

The son of Irish immigrants and bardic descendant of many a workingman, my father looked like he was a half second away from falling off the rickety old ladder -- either him or the tray of Prussian Wildflower.

"Do we have any more 7-Up?"

Dad concentrated on his next swab of the roller. His somewhat long and unkempt beard, a poet's beard, bobbed precariously close to the wall.

"Dad?"

He grunted. He smoothed the roller down, then over, making a reverse blue cloud in a white sky. "Try the garage."

Copyright © 2006 Aurelie Sheehan

From the book History Lesson for Girls by Aurelie Sheehan Published by Penguin; June 2007;$14.00US/$17.50CAN; 978-0-14-311190-0 Copyright © 2006 Aurelie Sheehan

About the Author

Aurelie Sheehan is the author of the short story collection Jack Kerouac Is Pregnant and the novel The Anxiety of Everyday Objects. The director of the creative writing program at the University of Arizona, she has received a Pushcart Prize, a Camargo Fellowship, and the Jack Kerouac Literary Award. She lives in Tucson with her husband and daughter.

For more information, please visit www.aureliesheehan.com

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