What is the law that governs the reflection of a light ray off a flat surface?
θi = θr
The law of reflection states that: light incident on a reflective surface at some angle will bounce off at an equal angle of reflection, as measured from the normal.
What will the angle of reflection be for a light ray incident on a surface, making an angle of 35 degrees to the surface?
θr = 55 degrees
Remember: the angles of incidence and reflection must be measured relative to the surface's normal. 90 - 35 = 55. θi and θr are shown below.
Refraction is when a light ray crosses a boundary from one transparent medium to another.
When the light ray changes media it bends either towards or away from the normal, depending on the properties of the respective media.
The refractive index of a transparent medium is a unitless ratio of the speed of light in that medium compared to speed of light in a vacuum.
Index of refraction is defined as n = c/v
n = index of refraction of the medium
c = speed of light traveling through a vacuum
v = speed of light traveling through the medium
What is the approximate index of refraction of:
Air: approximately 1
Water: approximately 1.33 (or 4/3)
Glass: varies greatly, but 1.5 and 2 are commonly used values
Since the speed of light can never exceed c, the value for the index of refraction of any medium cannot be less than 1.
How is the path of a light ray affected when the ray crosses a boundary from air (low n) into glass (high n)?
When a light ray crosses from air into glass, it bends towards the normal of the surface once inside the glass.
Any boundary crossing into a medium with a higher index of refraction will cause light to bend towards the normal.
How is the path of a light ray affected when the ray crosses a boundary from glass into air?
When a light ray crosses from glass into air, it bends away from the normal of the surface in the air.
Any boundary crossing into a medium with a lower index of refraction will cause light to bend away from the normal.
Snell's law gives the direct relationship between angles of incidence and refraction, from a light ray crossing the boundary between media:
n1sin(θ1) = n2sin(θ2)
n1 = index of refraction on the incident side
θ1 = angle of incidence
n2 = index of refraction on the refraction side
θ2 = angle of refraction
critical angle θc
The critical angle θc is the angle of incidence in one medium at which the angle of refraction into the new medium would become 90 degrees or higher.
There is only a critical angle for refraction across a boundary at which the index of refraction decreases, such as glass into air.
What is the formula for calculating the critical angle θc for a refraction from a medium with index n1 to a medium with index n2?
θc = sin-1(n2/n1)
From Snell's law:
n1sin(θc) = n2sin(90)
n1sin(θc) = n2(1)
sin(θc) = n2/n1
θc = sin-1(n2/n1)
total internal reflection
When a light ray approaches a boundary of decreasing index of refraction at an angle of incidence greater than the critical angle, it undergoes total internal reflection.
The light ray entirely reflects, staying in the incident medium. No light refracts across the boundary.
Under what conditions does total internal reflection occur?
For total internal reflection to occur, two conditions must be met:
- The index of refraction must decrease across the boundary in the direction of light refraction.
- The angle of incidence of the light ray must exceed the critical angle of the interface.
Dispersion is different wavelengths of light refracting at different angles.
The most common example of dispersion tested on the AP Physics exam is white light splitting into a spectrum of colors inside a prism and spreading out at a range of angles.
Why is a beam of sunlight separated into a rainbow of different colors as it passes through a prism?
The rainbow occurs due to dispersion.
The white sunlight beam is made up of all the colors of visible light mixed together, as is all white light. The glass of the prism is dispersive, and different colors of light refract differently as they pass through the prism, so they are separated upon exiting the back surface.
Blue light is refracted more than red light in glass.
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).
the focal point of an optic
An optic's focal point is the location where all rays parallel to the principal axis of the optic will cross after reflecting from/refracting through the optic.
An optic with a short focal point is a strong optic, bending light severely, while an optic with a long focal point is a weak optic, affecting light rays less significantly.
the image of an optical system
The image of an optical system is an optical reproduction of a physical object, formed when light rays transmitted by the object are caused to converge at a specific point by an optic or series of optics.
Many optics problems will involve calculating the location of the system's image, given a particular object and lens or mirror.
What are the characteristics of the parallel ray in an optical system?
The parallel ray is a light ray which reflects off the top of an object, and travels parallel to the principal axis of the optic.
After reflecting off/refracting through the optic, the parallel ray crosses the principal axis at the focal point, and can be used to help locate the image.
What are the characteristics of the focal ray in an optical system?
The focal ray is a light ray which reflects off the top of an object, and travels through the focal point of the optic.
After reflecting off/refracting through the optic, the focal ray emerges parallel to the principal axis of the optic, and can be used to help locate the image.
What are the characteristics of the center ray in an optical system?
The center ray is a light ray which reflects off the top of an object, and impacts the optic directly in the center.
The center ray is undeflected by reflecting off/refracting through the optic. It travels in a straight line, and can be used to help locate the image.
What makes a mirror converging?
A mirror is converging if any inbound light ray which is parallel to the mirror's principal axis crosses the axis after reflecting off the mirror.
Converging mirrors are concave in shape.
What is the radius of curvature of a converging mirror?
The radius of curvature of a mirror is the radius of the sphere of which the mirror is a small portion.
How does the radius of curvature of a converging mirror compare to the mirror's focal length?
For all spherical mirrors, the focal length is one-half the radius of curvature.
When is the image of an optical system real?
An optical system projects a real image when light rays reflected off/transmitted through the optic cross after the reflection/transmission.
Examples of real images include the images on movie screens and the image your eye produces on your retina.
When is the image of an optical system virtual?
An optical system projects a virtual image when light rays reflected off/transmitted through the optic are diverging away from one another.
Examples of virtual images include the images created by flat mirrors and magnifying glasses.
An optical system consists of an object and a single converging mirror. If the object is a distance between f and 2f from the optic, what are the properties of the final image?
The image is further from the optic than the object is, and the image is real, magnified, and inverted.
Find where the parallel, focal, and center rays cross after reflecting off the mirror to locate the image. Since the rays cross after reflection, the image is real.
An optical system consists of an object and a single converging mirror. If the object is at the focal length f, what are the properties of the final image?
No image is formed.
The parallel and center rays are parallel to one another after reflecting off the mirror. Since the rays never cross after reflection, no image is formed.
An optical system consists of an object and a single converging mirror. If the object is inside the focal length f, what are the properties of the final image?
The image is further from the optic than the object is, and the image is virtual, magnified, and upright.
The parallel and center rays are diverging after reflecting off the mirror. To locate the image, the rays much be projected behind the mirror to the point where they cross. Since only the virtual rays cross, the image is virtual.
What is the image equation (also known as the lens equation) used to calculate?
The image equation relates an optical system's focal length to its object and image distance.
The image equation reads:
1/f = 1/o + 1/i
f = focal length of the optic (lens or mirror)
o = distance between optic and object
i = distance between optic and image
What is the focal length of a converging mirror?
The focal length is the distance from the mirror to the focal point. Rays parallel to the optical axis cross at the focal point after reflecting off the mirror.
The focal length of any spherical optic is one-half its radius of curvature.