Light and Optics for the MCAT: Everything You Need to Know
/Learn key MCAT concepts about light and optics, plus practice questions and answers
(Note: This guide is part of our MCAT Physics series.)
Table of Contents
Part 1: Introduction to light and optics
Part 2: Characteristics of light
a) Photons
b) Double- and single-slit experiments
c) Reflection, refraction, and Snell’s law
d) Additional phenomena
Part 3: Mirrors
a) Flat mirrors
b) Spherical mirrors
Part 4: Thin lenses
a) Convex and concave lenses
b) Combining lenses
Part 5: High-yield terms and equations
Part 6: Passage-based questions and answers
Part 7: Standalone questions and answers
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Part 1: Introduction to light and optics
In this guide on light and optics, we will study the characteristics of light: including its trajectory and propagation. Light and optics are important for light-related reactions and many precision instruments you might find in a lab. For this reason, it is considered to be a medium-yield topic on the MCAT. In all likelihood, when it does come up on the MCAT, it will be in a strictly biological context as opposed to the physics and mathematical contexts in the sections below. However, understanding the fundamentals of this field will make understanding light and optics in relation to biology much smoother.
Below, the most important terms are in bold font. Be sure to understand these terms and use them to create your own examples. At the end of this guide, you will also find an MCAT-style practice passage and standalone questions. Practicing with these questions will not only test your knowledge of light and optics but also show you how the AAMC likes to ask questions.
Let’s get started!
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Part 2: Characteristics of light
Light is an electromagnetic wave of any wavelength. The electromagnetic spectrum—and therefore, what can be categorized as light waves—includes waves of all wavelengths, from radio frequencies to x-rays. Visible light, the light that makes up all the colors you see, only includes light in a small range of wavelengths (about 400-700 nanometers).
a) Photons
Recall that an electromagnetic wave is a wave composed of perpendicularly oscillating electric and magnetic fields. The two fields interact with each other and propagate light in the direction perpendicular to both oscillations.
Figure: Light is an electromagnetic wave.
However—perhaps the biggest “however” in physics—light can also be understood as a particle instead of a wave. A photon is a massless particle that represents a discrete unit (or a “quantum”) of light. We will use photons as a representation of light when considering the energy absorbed from light striking an object.
When objects absorb energy from incident light, they can only do so in discrete amounts. This discretized unit is called the photon energy. It is proportional to the frequency of light.
$$ E=h\times f $$ $$ \mbox{where E = photon energy,}$$ $$ \mbox{f = frequency}, $$ $$ \mbox{and h =} \textbf{Planck's constant, } 6.63\times 10^{-34}\space J\cdot s $$
Note that frequency and wavelength are inversely proportional: or that$$ \lambda = \frac{\nu}{f} $$ $$ \mbox{where } \lambda \mbox{ = wavelength,}$$ $$ \nu \mbox{ = the speed of light}, $$ $$ \mbox{and f = frequency} $$
Thus, light with high-frequency wavelengths has more energy than light with low-frequency wavelengths.
If the wave-particle duality of light doesn’t sit well with you, that’s completely fine! It is a debate that continues to puzzle many physicists today. This information is simply meant to prepare you for the different representations of light that will come later. Some applications will treat light as a wave, and others as a linearly moving particle.
b) Double- and single-slit experiments
All forms of waves share some similarities in their behavior. Interference occurs when two waves collide and combine. Constructive interference occurs when waves are in phase, and sum to make waves with a larger amplitude. Destructive interference occurs when waves are out of phase and cancel each other out to form a wave with zero amplitude. (For more information on this, be sure to refer to our guide on waves and sound.)
Figure: Two waves of equal amplitude traveling in opposite directions exhibiting constructive interference.
Figure: Two waves of opposite amplitude traveling in opposite directions exhibiting destructive interference.
As light can be considered as a wave, they also exhibit interference. This phenomenon was first observed during Thomas Young’s double-slit experiment. The results of this experiment led scientists to believe that light behaves as a wave.
In the double-slit experiment, light is shone through two narrow slits placed close together. After passing through the slits, the light strikes a wall and shows alternating bright spots and shadows—a pattern indicative of interference. The “maxima,” or bright spots, are areas of constructive interference. The “minima,” or shadows, are areas of destructive interference.
Figure: The double-slit experiment.
$$ d \times sin\theta = m \times \lambda $$ $$ \mbox{ where d = distance between the slits,} $$ $$ \theta= \mbox{ angle (from horizontal) to a location on the wall,} $$ $$ \mbox{m = a numerical multiple,} $$ $$ \mbox{and } \lambda \mbox{ = wavelength of the incoming light}$$
Take a moment to match the different terms in the equation to the image above it. While you won’t be expected to apply this equation on the MCAT, it’s useful to understand each variable.
Note that for any interference to occur, the light sources must be coherent, meaning the waves are in-phase. This is satisfied in the double-slit experiment because the light coming through each slit is generated by the same source and therefore must maintain the same phase relationship and amplitude. The other condition for interference is that the light must be monochromatic, meaning it consists of only one frequency or color.
What happens when we change the orientation of these two slits? A screen with many slits evenly spaced and placed close together is called a diffraction grating. The bright spots and dark spots from a diffraction grating are more intense, and the transition between them is more abrupt. The bright spots are relatively narrow, while the dark spots are wider.
In contrast to the double-slit experiment, in the single-slit experiment, light is shone through a single slit. Since there is only one slit, only one beam of light is allowed through. The waves of light passing through this slit are still able to constructively and destructively interfere with each other. The resulting diffraction pattern from a single slit appears to be more generally dispersed than the pattern resulting from a double slit.
c) Reflection, refraction, and Snell’s law
Light interacts with solids and objects in different ways. Reflection occurs when light bounces off of a surface. There are two types of reflection: specular reflection and diffuse reflection.
Specular reflection occurs when light reflects off a smooth surface at a definite angle. The simplest form of specular reflection occurs when light is shone perpendicularly at a surface. After it hits the surface, it is reflected back in the same direction it came from.
When light is shone at an angle, the same concept is at work. To understand this, decompose the initial vector of light into two components. After the reflection, the component pointing perpendicular to the wall reverses its direction. The component pointing parallel to the wall stays the same.
Figure: Reflection reverses the component of light perpendicular to the wall.
A simpler way to think about this is to say that the angle of incidence equals the angle of reflection. (Note that these angles are both measured with respect to the dashed perpendicular line.)
Figure: The angle of incidence is equal to the angle of reflection.
Diffuse reflection occurs when light bounces off a rough surface. The light penetrates into the microscopic crevices of the surface before undergoing normal speculative reflection. Since the microscopic surfaces face in essentially random directions, light reflects off the surface in all directions—rather than just the one that preserves the initial angle of incidence.
Figure: Diffuse reflection results in light being reflected at many angles.
These two forms of reflection explain why mirrors and white pieces of paper don’t appear to be the same. They both reflect all wavelengths of visible light. However, mirrors cause specular reflection that preserves the shape and location of incident light, while white pieces of paper only reflect white light in a diffuse manner.
In contrast to the behavior of light when it strikes a solid surface, light engages in refraction when it passes through different mediums.
$$ n = \frac{c}{v} $$ $$ \mbox{ where c = the speed of light in a vacuum,} $$ $$ \mbox{v = speed of light in a new medium}$$
Note that this implies that n must always be greater than 1, as light cannot travel faster than it does in a vacuum (or v cannot be larger than c). However, it is fine to approximate the refractive index of air as 1, as the speed of light in air is nearly identical to the speed of light in a vacuum.
You may be familiar with refraction in your everyday life. Consider a drinking straw placed in a glass of water. When light is shone perpendicularly through the glass, it will continue to travel straight through the glass at a lower velocity. However, if the light hits the glass at an angle, things become more complicated. The proportion of light’s velocity components changes, which means that the light—and the straw it has reflected off of—appears to “bend.”
When light crosses from one material to another, this apparent “bending” is described by Snell’s law,
$$ n_1\times sin\theta_1 = n_2 \times sin\theta_2$$ $$ \mbox{where } n_1 \mbox{ = the index of refraction of the first material,} $$ $$ \theta_1 \mbox{ = the angle of incidence (from the normal),}$$ $$ n_2 \mbox{ = the index of refraction of the second material,} $$ $$ \theta_2 \mbox{ = the angle of refraction (from the normal)} $$
Figure: The quantities involved in Snell’s law.
$$ \frac{n_1}{n_2} = \frac{sin \theta_2}{sin \theta_1} $$
Materials such as water and glass usually transmit much of the light incident on them. However, at certain angles of incidence, a ray of light won’t penetrate them at all and will instead just skip off the surface. In these cases, all of the incident light is reflected—even by materials that may be transparent or translucent. This phenomenon is called total internal reflection.
$$ n_1 \times sin\theta_c = n_2 \times sin(90^{\circ}) $$ $$\mbox{where } n_1 \mbox{ = the index of refraction of the first material,} $$ $$ \theta_c \mbox{ = the critical angle (measured from the normal),} $$ $$ n_2 \mbox{ = the index of refraction of the second material} $$
d) Additional phenomena
Recall that light is an electromagnetic wave. Different wavelengths correspond to different types of light. Red light has a longer wavelength than blue light, which has a longer wavelength than x-rays.
As it turns out, the speed of light in some materials depends on the wavelength. Light of different wavelengths or different colors has different indices of refraction. The shorter the wavelength, the more the light will bend.
The result of these different refraction indices is dispersion. Different wavelengths of light will separate themselves and spread out when they enter a new material.
Figure: A rainbow appears in a prism due to the dispersion of white light.
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