Physics -- Ch. 27 Conceptual

What type of experimental evidence indicates that light is a wave?

The primary experimental evidence that light is a wave is the observation of interference and diffraction. (Young’s double slit experiment).

Under what conditions can light be modeled like a ray? Like a wave?

• Ray Model: Light can be modeled as a ray (geometric optics) when the dimensions of the objects it interacts with are significantly larger than its wavelength (e.g., mirrors, large lenses).

• Wave Model: Light must be modeled as a wave when it interacts with objects or openings that are comparable to or smaller than its wavelength, leading to phenomena like diffraction and interference.

Go outside in the sunlight and observe your shadow. It has fuzzy edges even if you do not. Is this a diffraction effect? Explain.

No, the fuzzy edges (penumbra) of your shadow in sunlight are primarily not a diffraction effect. 

Because the Sun is an extended source (not a point source), light from different parts of the Sun's disk is partially blocked by your body, creating a gradient from light to dark at the edges. While diffraction does occur at any edge, it is negligible at this scale compared to the penumbra effect.

Does Huygens’s principle apply to all types of waves?

Yes, Huygens's principle applies to all types of waves, including mechanical waves (sound, water) and electromagnetic waves (light). It states that every point on a wavefront acts as a source of spherical secondary wavelets.

Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

No, two independent sources like car headlights will not produce an interference pattern. For interference to occur, sources must be coherent (constant phase relationship). Independent sources emit light with random, rapidly changing phases, causing the interference pattern to shift so quickly that it averages out to a uniform illumination.

What is the advantage of a diffraction grating over a double slit in dispersing light into a spectrum?

The primary advantage is that diffraction gratings produce much sharper and more widely spaced maxima than a double slit. Because a grating has thousands of slits, constructive interference occurs only at very precise angles, allowing for higher resolution and better separation of different wavelengths in a spectrum.

Suppose a feather appears green but has no green pigment. Explain in terms of diffraction.

This is due to iridescence caused by thin-film interference or diffraction. The microscopic structure of the feather (like tiny barbs) acts as a diffraction grating or a series of thin layers. These structures reflect light such that only the green wavelength undergoes constructive interference, while other colors interfere destructively.

As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?

As the slit width is reduced, the diffraction pattern spreads out. According to the formula sin(angle)= m(wavelength) / a… a smaller a results in a larger angle for the minima, making the central maximum wider and the overall pattern less intense.

How is the difference in paths taken by two originally in-phase light waves related to whether they interfere constructively or destructively? How can this be affected by reflection? By refraction?

• Constructive Interference: Occurs when the path difference is an integer multiple of the wavelength.

• Destructive Interference: Occurs when the path difference is a half-integer multiple.

• Reflection: If light reflects off a medium with a higher refractive index, it undergoes a phase shift.

• Refraction: Changes the wavelength, altering the optical path length even if the physical distance remains the same.

Is there a phase change in the light reflected from either surface of a contact lens floating on a person’s tear layer? The index of refraction of the lens is about 1.5, and its top surface is dry.

The lens has n=1.5, air has n=1, and tears have n=1.33.

• Top surface (Air to Lens): n(air) < n(lens), so there is a phase change.

• Bottom surface (Lens to Tears): n(lens) > n(tears), so there is no phase change

In placing a sample on a microscope slide, a glass cover is placed over a water drop on the glass slide. Light incident from above can reflect from the top and bottom of the glass cover and from the glass slide below the water drop. At which surfaces will there be a phase change in the reflected light?

• Top of glass cover (Air to Glass): Phase change (low to high)

• Bottom of glass cover (Glass to Water): No phase change (high to low).

• Top of slide (Water to Glass): Phase change (low to high)

Under what circumstances is the phase of light changed by reflection? Is the phase related to polarization?

Phase changes occur during reflection when light travels from a medium with a lower refractive index to one with a higher refractive index. The phase change is not directly related to polarization in terms of its existence, but the amount of light reflected (reflectivity) depends on polarization and the angle of incidence (e.g., Brewster’s angle).

Can a sound wave in air be polarized? Explain.

No, sound waves in air cannot be polarized. Polarization is a property of transverse waves (where oscillation is perpendicular to travel). Sound in air is a longitudinal wave (oscillation is parallel to travel), so it has no directional orientation to "filter."

No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

When a third filter is placed at an angle (e.g., 45) between two crossed filters, it reorients the polarization vector of the light. The first filter polarizes light vertically; the middle filter rotates a component of that light to 45; the final horizontal filter then allows the horizontal component of that light to pass. Most light passes when the middle filter is at exactly 45.

Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

The energy is absorbed by the polarizing filter and converted into thermal energy (heat). The long-chain molecules in the filter conduct electricity in response to the light's electric field, and the resulting resistance dissipates the energy as heat.

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to 1/𝜆4. Does this mean there is more scattering for small 𝜆 than large 𝜆? How does this relate to the fact that the sky is blue?

Yes, there is significantly more scattering for small (shorter wavelengths). Since scattering is proportional to 1/h^4, blue and violet light are scattered much more efficiently than red light. This is why the sky appears blue.

Using the information given in the preceding question, explain why sunsets are red.

Sunsets are red because, at sunset, sunlight must travel through a much greater thickness of the Earth's atmosphere to reach our eyes compared to when the sun is overhead, causing shorter wavelengths (blue and violet) to be completely scattered away by air molecules and dust, while longer wavelengths (reds and oranges) pass through to be seen.