MCAT Physics and Math Review

Chapter 8: Light and Optics

Conclusion

This chapter illuminated the key behaviors and characteristics of light and optical systems. First, we described the nature of the electromagnetic (EM) wave, noting that we can only perceive light in the visible range (400–700 nm). We then focused on geometrical optics to consider the reflective and refractive behaviors of light, noting the ways in which mirrors reflect light to produce images and lenses refract light to produce images. We acknowledged the fact that light doesn’t always travel in straight-line pathways but can bend and spread out through diffraction. We examined the pattern of interference that occurs when light passes through a double slit, as demonstrated in Young’s double-slit experiment. Finally, we wrapped up with a discussion on plane-polarized and circularly polarized light. In this chapter, we considered the properties that support the wave theory of light. In the next chapter, we’ll explore the photon and properties that support the particle theory of light, as well as other atomic and nuclear phenomena.

Concept Summary

Electromagnetic Spectrum

·        Electromagnetic waves are transverse waves that consist of an oscillating electric field and an oscillating magnetic field.

·        The two fields are perpendicular to each other and to the direction of propagation of the wave.

·        The electromagnetic spectrum is the range of frequencies and wavelengths found in EM waves.

·        The EM spectrum includes, from lowest to highest energy, radio wavesmicrowavesinfrared, visible light, ultraviolet, x-rays, and γ-rays.

·        The visible spectrum runs from approximately 400 nm (violet) to 700 nm (red).

Geometrical Optics

·        Reflection is the rebounding of incident light waves at the boundary of a medium.

·        The law of reflection states that the incident angle will equal the angle of reflection, as measured from the normal.

·        Spherical mirrors have centers and radii of curvature as well as focal points.

o   Concave mirrors are converging systems and can produce realinverted images or virtualupright images, depending on the placement of the object relative to the focus.

o   Convex mirrors are diverging systems and will only produce virtual, upright images.

o   Plane mirrors also produce virtual, upright images; these images are always the same size as the object. They may be thought of as spherical mirrors with infinite radii of curvature.

·        Refraction is the bending of light as it passes from one medium to another.

·        The speed of light changes depending on index of refraction of the medium. This speed change causes refraction.

·        The amount of refraction depends on the wavelength of the light involved; this behavior causes dispersion of light through a prism.

·        Snell’s law (the law of refraction) states that there is an inverse relationship between the index of refraction and the sine of the angle of refraction (measured from the normal).

·        Total internal reflection occurs when light cannot be refracted out of a medium and is instead reflected back inside the medium.

o   This happens when light moves from a medium with a higher index of refraction to a medium with a lower index of refraction with a high incident angle.

o   The minimum incident angle at which total internal reflection occurs is called the critical angle.

·        Lenses refract light to form images of objects.

o   Thin symmetrical lenses have focal points on each side.

o   Convex lenses are converging systems and can produce real, inverted images or virtual, upright images.

o   Concave lenses are diverging systems and will only produce virtual, upright images.

o   Lenses with non-negligible thickness require use of the lensmaker’s equation.

Diffraction

·        Diffraction is the bending and spreading out of light waves as they pass through a narrow slit.

·        Diffraction may produce a large central light fringe surrounded by alternating light and dark fringes with the addition of a lens.

·        Interference supports the wave theory of light.

·        Young’s double-slit experiment shows the constructive and destructive interference of waves that occur as light passes through parallel slits, resulting in minima (dark fringes) and maxima (bright fringes) of intensity.

Polarization

·        In plane-polarized light, all of the light rays have electric fields with parallel orientation.

·        Plane-polarized light is created by passing unpolarized light through a polarizer.

·        In circularly polarized light, all of the light rays have electric fields with equal intensity but constantly rotating direction.

·        Circularly polarized light is created by exposing unpolarized light to special pigments or filters.

Answers to Concept Checks

·        8.1

1.    γ-rays > x-rays > ultraviolet > visible light > infrared > microwaves > radio. Frequency follows the same trend as energy, whereas wavelength follows the opposite trend.

2.    False. Light waves are transverse because the direction of propagation is perpendicular to the direction of oscillation.

3.    Visible light ranges from wavelengths of about 400 nm to 700 nm. This is in comparison to the entire EM spectrum which ranges from wavelengths of nearly 0 to 109 m.

·        8.2

1.     

Mirrors

Symbol

Positive

Negative

o

Object is in front of mirror

Object is behind mirror (extremely rare)

i

Image is in front of mirror (real)

Image is behind mirror (virtual)

r

Mirror is concave (converging)

Mirror is convex (diverging)

f

Mirror is concave (converging)

Mirror is convex (diverging)

m

Image is upright (erect)

Image is inverted

Lenses

Symbol

Positive

Negative

o

Object is on same side of lens as light source

Object is on opposite side of lens from light source (extremely rare)

i

Image is on opposite side of lens from light source (real)

Image is on same side of lens as light source (virtual)

r

Lens is convex (converging)

Lens is concave (diverging)

f

Lens is convex (converging)

Lens is concave (diverging)

m

Image is upright (erect)

Image is inverted

2.    True. In optics, incident angles are always measured relative to the normal.

3.    Light will bend toward the normal when going from a medium with low n to high n. Light will bend away from the normal when going from a medium with high n to low n; if the incident angle is larger than the critical angle (θc), total internal reflection will occur.

4.    Dispersion is the tendency for different wavelengths of light to experience different degrees of refraction in a medium, leading to separation of light into the visible spectrum (a rainbow). Aberration (spherical or chromatic) is the alteration or distortion of an image as a result of an imperfection in the optical system.

5.     and 

·        8.3

1.    Diffraction through a single slit does not create characteristic fringes when projected on a screen, although the light does spread out. When a lens is introduced into the system, the additional refraction of light causes constructive and destructive interference, creating fringes.

2.    Fringes result from constructive and destructive interference between light rays.

3.    The image formed during double-slit diffraction contains fringes because light rays constructively and destructively interfere. A single slit forms an image of a wide band of light, spread out from its original beam.

4.    True. Maxima and minima alternate in a diffraction pattern. A maximum is equidistant between two minima, and a minimum is equidistant between two maxima.

·        8.4

1.    Plane-polarized light contains light waves with parallel electric field vectors. Circularly polarized light selects for a given amplitude and has a continuously rotating electric field direction.

2.    Plane polarization has no effect on the wavelength (or frequency or speed) of light. Polarization does affect the amount of light passing through a medium and light intensity.

Equations to Remember

(8.1) Speed of light from frequency and wavelength: c = fλ

(8.2) Law of reflectionθ1 = θ2

(8.3) Optics equation

(8.4) Magnification

(8.5) Index of refraction

(8.6) Snell’s lawn1 sin θ1 = n2 sin θ2

(8.7) Critical angle

(8.8) Lensmaker’s equation

(8.9) Power

(8.10) Focal length of multiple lens system

(8.11) Power of multiple lens systemP = P1 + P2 + P3 + ··· + Pn

(8.12) Magnification of multiple lens systemm = m1 × m2 × m3 × ··· × mn

(8.13) Positions of dark fringes in slit–lens setupa sin θ = nλ

(8.14) Positions of dark fringes in double-slit setup

Shared Concepts

·        Behavioral Sciences Chapter 2

o   Sensation and Perception

·        Biochemistry Chapter 3

o   Nonenzymatic Protein Function and Protein Analysis

·        Organic Chemistry Chapter 2

o   Isomers

·        Organic Chemistry Chapter 11

o   Spectroscopy

·        Physics and Math Chapter 7

o   Waves and Sound

·        Physics and Math Chapter 9

o   Atomic and Nuclear Phenomena