MCAT Physics and Math Review
Chapter 8: Light and Optics
The next time you’re browsing your local convenience store, take a look at the security mirrors—the ones that bulge out from the wall, usually above eye level. Looking into one of these mirrors, notice not just that the image you see of the world is distorted but how it is distorted: the image is still right-side up, but everything is much smaller than you’d expect, and the curve of the mirror introduces some slopes that are not present in reality. Additionally, you see a much wider field of vision than you would if the mirror were a simple plane mirror. This is why security mirrors are useful: they are a convenient, low-tech solution that allows the cashier to survey the entire store in one glance. All these features result from the fact that the security mirror is a convex, diverging optical system. Parallel light rays that hit the mirror are reflected in multiple directions, which allows observers to see a large field of vision, even if the image is somewhat distorted and the objects in the image are closer than they appear. Indeed, the passenger-side mirror of a car that bears that same message is also a convex mirror, allowing the driver to see a wider view of the cars behind him or her.
This chapter will first complete a topic from Chapter 7 of MCAT Physics and Math Review by analyzing the transverse waveform of visible light and other electromagnetic (EM) waves. We will then consider in detail the rules of optics, which describe the behavior of electromagnetic waves as they bounce off of and travel through various shapes and compositions of matter. The optical systems covered are those tested on the MCAT: concave and convex mirrors, which produce images by reflection, and concave and convex lenses, which produce images by refraction. To finish, we will discuss the phenomena of thin-slit experiments (diffraction) and light polarization.
8.1 Electromagnetic Spectrum
The full electromagnetic spectrum includes radio waves on one end (long wavelength, low frequency, low energy) and gamma rays on the other (short wavelength, high frequency, high energy). Between the two extremes, we find, in order from lowest energy to highest energy,microwaves, infrared, visible light, ultraviolet, and x-rays. This chapter will focus primarily on the range of wavelengths corresponding to the visible spectrum of light (400 nm to 700 nm).
A changing magnetic field can cause a change in an electric field, and a changing electric field can cause a change in a magnetic field. Because of the reciprocating nature of these two fields, we can see how electromagnetic waves occur in nature. Each oscillating field causes oscillations in the other field completely independent of matter, so electromagnetic waves can even travel through a vacuum.
Electromagnetic waves are transverse waves because the oscillating electric and magnetic field vectors are perpendicular to the direction of propagation. The electric field and the magnetic field are also perpendicular to each other. This is illustrated in Figure 8.1.
Figure 8.1. Electromagnetic Wave The electric field (E) oscillates up and down the page; the magnetic field (B) oscillates into and out of the page.
The electromagnetic spectrum describes the full range of frequencies and wavelengths of electromagnetic waves. Wavelengths are often given in the following units: mm (10–3 m), µm (10–6 m), nm (10–9 m), and Å (ångström, 10–10 m). The full spectrum is broken up into many regions, which in descending order of wavelength are radio (109–1 m), microwave (1 m–1 mm), infrared (1 mm–700 nm), visible light (700–400 nm), ultraviolet (400–50 nm), x-ray (50–10–2 nm), and γ-rays (less than 10–2 nm). The electromagnetic spectrum is depicted in Figure 8.2.
Figure 8.2. The Electromagnetic Spectrum
Electromagnetic waves vary in frequency and wavelength, but in a vacuum, all electromagnetic waves travel at the same speed, called the speed of light. This constant is represented by c and is approximately To a first approximation—and for the purposes of all MCAT-related equations—electromagnetic waves also travel in air with this speed. In reference to electromagnetic waves, the familiar equation ν = fλ becomes
c = fλ
where c is the speed of light in a vacuum and, to a first approximation, also in air, f is the frequency, and λ is the wavelength.
To recall the order of the colors in the visible spectrum, remember the grade-school “rainbow” of ROY G. BIV (red, orange, yellow, green, blue, indigo, violet).
COLOR AND THE VISIBLE SPECTRUM
The only part of the spectrum that is perceived as light by the human eye is the visible region. Within this region, different wavelengths are perceived as different colors, with violet at one end of the visible spectrum (400 nm) and red at the other (700 nm).
Wavelengths in the visible range are common on the MCAT. Remembering the boundaries of the visible spectrum (about 400–700 nm) will save you time and energy on Test Day.
Light that contains all the colors in equal intensity is perceived as white. The color of an object that does not emit its own light is dependent on the color of light that it reflects. Thus, an object that appears red is one that absorbs all colors of light except red. This implies that a red object under green illumination will appear black because it absorbs the green light and has no light to reflect. The term blackbody refers to an ideal absorber of all wavelengths of light, which would appear completely black if it were at a lower temperature than its surroundings.
MCAT Concept Check 8.1:
Before you move on, assess your understanding of the material with these questions.
1. Order the types of electromagnetic radiation from highest energy to lowest energy. What other property of light follows the same trend?
· Also follows the same trend:
2. True or False: Light waves are longitudinal because the direction of propagation is perpendicular to the direction of oscillation.
3. What are the boundaries of the visible spectrum? How does the range of the visible spectrum compare to the range of the full electromagnetic spectrum?