Light & Optics Flashcards
Always a favorite of MCAT test-makers, optical systems have become especially high-yield due to their applications to biological systems. Use these cards to master Snell’s law, diverging and converging mirrors, and combinations of lenses. For enhanced practice, think about how these concepts relate to biological systems, such as the human eye.
What law gives the angle of reflection of a light ray from a flat surface?
θi = θr
This expression is the law of reflection, which states that the angle of incidence will equal the angle of reflection for a light ray striking a surface. Note that all angles are measured from the normal.
A light ray strikes a pane of glass, making an angle of 35º with the surface. Find the angle of reflection.
θr = 55º
The angle of incidence always equals the angle of reflection. However, remember that the angles of incidence and reflection must be measured relative to the normal. If the angle made with the surface is 35º, the angle made with the normal will be (90º - 35º) = 55º. θi and θr are shown below.
Define:
refraction
Refraction occurs when a light ray crosses a boundary from one transparent medium to another.
When a light ray travels between media, it will bends either toward or away from the normal, depending on the properties of the media involved.
Define:
index of refraction
The index of refraction (n) of a transparent medium is a unitless ratio of the speed of light in that medium compared to the speed of light in a vacuum.
Index of refraction is defined as n = c/v. Here, n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the medium.
What are the approximate indices of refraction of air, water, and glass, respectively?
- nair = approximately 1
- nwater = approximately 1.33
- nglass varies greatly, but 1.5 is a commonly-used value on the MCAT
What features characterize substances with indices of refraction that are less than 1?
No substance has an n value that is less than 1.
Index of refraction is defined as c/v, where c is light’s speed in a vacuum and v is its speed in the relevant medium. Since light travels fastest in a vacuum, n is always equal to or greater than 1.
How does the path of a light ray change when it crosses a boundary from air into glass?
When a light ray travels from air into glass, it bends toward the normal of the surface.
Air has a lower index of refraction than glass. Whenever light moves from lower to higher index of refraction, it will angle toward the normal.
How does the path of a light ray change when it crosses a boundary from water into air?
When a light ray travels from water into air, it bends away from the normal of the surface.
Water has a higher index of refraction than air. Whenever light moves from higher to lower index of refraction, it will angle away from the normal.
What quantities are related by Snell’s law?
Snell’s law gives the relationship between the angle of incidence and that of refraction for a light ray crossing the boundary between media. The equation is:
n1sin(θ1) = n2sin(θ2)
where
n1 = index of refraction on the incident side
θ1 = angle of incidence
n2 = index of refraction on the refraction side
θ2 = angle of refraction
What is the critical angle (θc)?
The critical angle (θc) is the angle of incidence in a certain medium at which the angle of refraction into a new medium would reach 90º. Angles larger than the critical angle will result in total internal reflection.
A critical angle only exists when light is moving from a high to a low index of refraction. A classic example is refraction from diamond into air.
What formula is used to calculate the critical angle (θc)? Assume that light is traveling from a medium with refractive index n1 to a medium with index n2.
θc = sin-1(n2/n1)
This formula can be derived from Snell’s law:
n1sin(θc) = n2sin(90º)
n1sin(θc) = n2(1)
sin(θc) = n2/n1
θc = sin-1(n2/n1)
The utility of a fiber optic cable depends on its ability to trap light inside its own material for long distances. What property is likely involved in this example?
Fiber optic cables rely on total internal reflection.
In such cases, light rays stay entirely in the incident medium; no light refracts across the boundary. This only occurs if the n value of the cable is sufficiently higher than that of the outside material, and if the angle of incidence is large enough.
Under what conditions does total internal reflection occur?
For total internal reflection to occur, two conditions must be met:
- Light must be traveling from high to low index of refraction.
- The angle of incidence of the light ray must exceed the critical angle of the interface.
Define:
dispersion
Dispersion involves the refraction of different wavelengths of light at different angles.
The most common example of dispersion tested on the MCAT involves white light traveling through a prism. When dispersion occurs, the light splits into a spectrum of colors and spreads out at a range of angles.
What process causes a beam of sunlight to separate into a rainbow of colors as it passes through a prism?
The rainbow is produced by dispersion.
Like all white light, sunlight is made up of all the colors of visible light mixed together. Different colors of light refract differently as they pass through the prism, so they are separated upon exiting the back surface.
When white light is separated by a prism into its component colors, in what order do they appear?
The separated colors are, in order, red, orange, yellow, green, blue, indigo, violet.
This is easily remembered by the mnemonic ROYGBIV (Roy Gee Biv). Note that violet light, which travels slowly and has a high frequency, bends the most while red light bends the least.
Define:
focal point
An optic’s focal point is the location where light rays parallel to its axis will cross after reflecting from, or refracting through, the optic.
An optic with a short focal point is strong and bends light drastically, while an optic with a long focal point is weak and affects light rays less significantly.
In an optical system, what is an image?
An image is an optical reproduction of a physical object, formed when light rays transmitted by the object are converged at a specific point by an optic or series of optics.
Many optics problems will involve calculating the location of a system’s image, given a particular object and a lens or mirror.
What types of lens or mirror has a radius of curvature?
All spherical lenses and mirrors have radii of curvature.
Specifically, the radius of curvature of a mirror is the radius of the sphere from which the mirror or lens is a small portion.
How does the radius of curvature of a lens or mirror compare to its focal length?
For all spherical lenses and mirrors, the radius of curvature is equal to twice the focal length.
In other words, focal length can be found by taking one-half of the radius of curvature.
Lenses A and B are both converging lenses. How will the strength of the two lenses compare if the radius of curvature of Lens A is significantly larger than that of Lens B?
Lens B will be stronger than Lens A.
Since Lens A has a larger radius of curvature, it must also have a larger focal distance. The larger the focal length, the farther away from the lens the image will be formed; a weak lens will therefore have a large focal length. This also relates to the equation P = 1/f, which shows that power decreases as focal length increases.
When is the image produced by an optical system real?
An optical system projects a real image when light rays reflected off or transmitted through the optic cross after the reflection or transmission.
Real images include the images on movie screens and the images made by the eye on the retina.
When is the image produced by an optical system virtual?
An optical system projects a virtual image when light rays reflected off or transmitted through the optic diverging away from one another.
Virtual images include the images created by flat mirrors and magnifying glasses.
In what cases will a virtual image be upright, or erect?
Any virtual image produced by any system will be upright.
Remember “IR” and “UV”; inverted images are always real, while upright images are always virtual.