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1º TESTE Fotónica em Materiais, 4 Abril 2016, ıÌAA ýùëO ØEI , corr. incorr. n/r

No. Nome Curso

(01) (02) (03) (04) (05) (06) (07) (08) (09) (10)

Notas - O teste tem a duração de 1H50 e é constituı́do por duas partes:PARTE 1 (12/20) - Para cada questão de escolha múltipla selecione a resposta correcta. Só são consideradas as respostas queestiverem indicadas na grelha de respostas e escritas a tinta. Cada questão respondida correctamente vale 1.5/20.PARTE 2 (8/20) - A resolução dos exercı́cios tem de ser apresentada com letra facilmente legı́vel, no espaço fornecido apóscada questão, caso contrário a resposta poderá não ser considerada. Cada questão tem a cotação máxima de 4/20.As folhas fornecidas não podem ser desagrafadas e devem ser devolvidas ao Docente presente na sala, mesmo que, eventual-mente, não queira quea sua provaseja classiicada. Todas as folhas têm de estar identiicadas com o nome e número de aluno.

1. Glass prims, with a frequency-dependent refractiveindex n, are used to disperse sunlight and split it in a

rainbow of colors. Which light travels faster inside theprisms, red or violet light? Why?A)n(violet) > n(red) → violet travels fasterB)n(red) > n(violet) → red travels fasterC)n(red) > n(violet) → violet travels fasterD)n(violet) = n(red) → violet and red travel at same speedE)n(violet) > n(red) → red travels faster

2. In a storm, we irst see the lightning and then hear thethunder. What type of waves do our senses detect?A)First a longitudinal and then a transverse waveB)Two transverse waves at the same timeC)Two transverse waves, one after the otherD)First a transverse and then a longitudinal waveE)Two longitudinal waves, one after the other

3. An inteferometer allows tuning the path difference (d),hence the phase shift, between two waves of wavelenght λ.When increasing d, the waves interfere constructively ford=d₁, and then anihilate each other for d=d₂. Therefore:A)d₁=λ/2 ; d₂=λ B)d₁=3λ/2 ; d₂=2λ C)d₁=λ ; d₂=3λ/2D)d₁=π; d₂=2πE)d₁=0 ; d₂=π/2

4. Monochromatic light with intensity  passes through asurface with   narrow equally-spaced slits. The conse-quent interference pattern is registered on a screen placedfar from the slits. Determine  knowing that the intensityof the maximum peak registered in the pattern is 100.A)N=1000B)N=10000C)N=10D)N=100E)N=1

5. A mass   attached to a spring of spring constant    isstretched a length     from its equilibrium position andreleased with no initial speed.What is the maximum speed attained by the mass in thesubsequent motion?A)  /B) /C)/()D)0.5

E) //

6. The momentum of Sunlight electromagnetic wavesproduces pressure at the Earth’s surface. The rate per unit area at which solar energy is delivered to Earth’s surface is

around 1000 W/m².What is the solar radiation pressure (in SI), assumingcomplete light absorption by the illuminated surface?A)3.33 mPaB)300 kPaC)3.33 PaD)3.33 μPaE)1 kPa

7. A mass   attached to a spring of spring constant    isstretched a length     from its equilibrium position andreleased with no initial speed.At what time is the maximum speed irst attained?

A)(/2) /B)/(2)C)(2)/()D)2 /E)2  /

8. The rate per unit area at which solar energy is deliveredto Earth’s surface is around 1000 W/m².Use this number to estimate the amplitude of the electricand magnetic ields in the electromagnetic waves that deliver this energy.A)E₀=0.88×10³ V/m ; B₀=0 T

B)E₀=4.4×10³ V/m ; B₀=0.15×10⁻⁴ TC)E₀=2.9×10⁵ V/m ; B₀=4.4×10² TD)E₀=0 V/m ; B₀=0.88×10³ TE)E₀=8.8×10² V/m ; B₀=2.9×10⁻⁶ T

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9. [PARTE 2 - ABERTA] A disturbance along a string hasa wave form that along a part of it takes the function(, ) = ( − ), where (,)   is the transversedisplacement of the string from the -axis. Here    is aconstant. The igure illustrates what is meant: The solidpart of the curve is the one we are concentrating on. Doesthis part of the disturbance satisfy the wave equation?Prove it.

10. [PARTE 2 - ABERTA] The soap bubble shown in crosssection in the igure has thickness and index of refraction. Light of wavelength  in air falls vertically ( = 0) onthe bubble and is relected back. (a) Express the conditionfor constructive interference for the relected light. (b)If   = 400 and  = 1.3, what color or colors (wave-lengths in the visible range) will interfere constructively inthe relected light?

NOTE: Light is affected by an 180° phase shift when it isrelected from a surface whose  is higher than that of themedium where it was traveling.

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