34. Wave Optics

Diffraction

Apertures and Diffraction - Exploring Wave Motion (3/5)

 You place one glass slide on top of another, with an animal hair between them at one end. You illuminate the slides with blue light of wavelength <math display=“inline”><mrow><mrow><mn>450</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nm</mi></mrow><mo>.</mo></mrow></math> You count along the slide and find 300 transitions from bright to dark and back to light. How thick is the hair? 

Wave Diffraction

 A diffraction grating has <math display=“inline”><mrow><mn>500</mn><mtext>&#x00A0;</mtext><mtext>lines</mtext><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi><mo>.</mo></mrow></math> If it is illuminated by a laser at <math display=“inline”><mrow><mrow><mn>532</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nm</mi></mrow><mo>,</mo></mrow></math> how many bright spots will be observed on a screen placed behind the grating? 

 A diffraction grating with <math display=“inline”><mrow><mn>500</mn><mtext>&#x00A0;</mtext><mtext>lines</mtext><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi></mrow></math> is illuminated by two wavelengths of light: <math display=“inline”><mrow><mrow><mn>450</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nm</mi></mrow></mrow></math> and <math display=“inline”><mrow><mrow><mn>600</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nm</mi></mrow><mo>.</mo></mrow></math> What is the distance between the <math display=“inline”><mrow><mi>m</mi><mo>=</mo><mn>2</mn></mrow></math> bright fringes of the two colors of light on a screen <math display=“inline”><mrow><mn>1</mn><mo>.</mo><mrow><mn>3</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> away? 

 A particular kind of oil with an index of refraction of <math display=“inline”><mrow><mn>1</mn><mo>.</mo><mn>46</mn></mrow></math> has spilled on water. The different thicknesses of the oil slick result in different colors being strongly reflected at different parts of the spill. But near the edges, you identify the thinnest part of the oil layer that strongly reflects green light with a wavelength of 550 nm when you are directly overhead. What is the thickness of the oil at this point? Assume light is incident normal to the oil surface. 

 A <math display="inline"><mrow><mn>480</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nm</mi></mrow></math> light is used to illuminate a diffraction grating with <math display="inline"><mrow><mn>500</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">lines</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi></mrow></math>. What is the angle, measured from the central maximum, to the m=3 bright fringe? 

 A carbon dioxide laser produces <math display='inline'><mrow><mn>10.6</mn><mo rspace="thickmathspace">&#x2062;</mo><mo mathvariant="normal" class="MathML-Unit">&#x03BC;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></math> electromagnetic waves, which pass through a circular aperture with diameter <math display="inline"><mrow><mn>1.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">mm</mi></mrow></math>. What is the approximate width of the laser beam when it strikes a target <math display="inline"><mrow><mn>3.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></math> away? 

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