Optics Lessons: Part 5 - Mirrors and Lenses
Lenses and mirrors play important roles in our daily lives even though we may not notice them. Even now, as you are reading this, you are using the cornea lens in each eye and if you use eyewear such as contacts or glasses, you are also those lenses to view this page. Recently you have probably seen your reflection in a mirror. In this lesson, we will explore different types of lenses and see how they impact vision.
A plane mirror has even surfaces. The normal is a line perpendicular to all points of a plane mirror. The angle of incidence is an angle that light hits the mirror relative to the normal. The angle of reflection is an angle of that light's reflection, on the other part of the normal, and is equal to the angle of incidence.
The image seen in a plane mirror seems to be behind the mirror. This is an example of a virtual image It is also right-side up, but reversed from right to left. This can be seem noticably by holding up a word to a plane mirror. The letters would each be flipped and the order of the word would be reversed.
To determine the size of an image seen through a plane mirror, the following equation is used:
A spherical mirror is a mirror in the form of a slice of a spherical surface.
A convex mirror is curved outward, like the outside of a sphere. When parallel light rays pass through a convex mirror, the reflected light appears to have come from behind, hence making it a virtual image. Because the rays reflected from a convex mirror diverge from any length, a diverging mirror will always produce a virtual image. This explains why the passenger side mirrors of cars, which are convex mirrors, display objects that look smaller than they are: the brain considers the diverging rays to have come from an image behind the mirror itself.
A concave mirror curves inward like the hollow inside of a sphere. Or, in other words, it appears "caved-in", which could help you differentiate from both spherical mirrors. The light hitting the surface of concave mirror converges, and the image made by the mirror is either virtual or real, depending on the position of the object that is reflected. If the object is between the mirror and the focus, it will be right side up, virtual, and larger, while objects farther than the focus will be real images that subject to the position once again, may appear upside-down, larger, or smaller.
Spherical Mirror Equations
Here are equations that analytically explain the image results discussed in the previous section.
The focal length of a spherical mirror:
The spherical mirror equation:
The magnification equation for a spherical mirror:
Note: If the magnitude, or the absolute value of M is greater than one, then the image is larger than the object, and if it is less than one, then the image is smaller than the object.
An optical lens is made from see-through materials and is generally spherical in shape.
Note: In this lesson, we will assume the lenses are thin lens, where the displacement of light as a result of refraction is so small, it can be ignored. Analyzing certain relationships with thick lens characteristics will be too complex because of the possibly large displacements resulting from the refraction from them.
Types of Lenses
Two types of lenses are biconvex lenses, which are converging lenses and biconcave lenses, which are diverging lenses. Converging lenses are thicker in the center than at the edges, while diverging lenses are thicker at the edges that in the center.
Let’s compare the images each type of lens produces:
Convex or converging lenses can form real or virtual images:
Concave or diverging lenses produce virtual images. The light rays appear to diverge from the virtual image on the side of the lens with the object.
As done previously with the mirrors section, here are equations that analytically explain the image results described above:
Where M is the magnification factor sobject is distance from object to the lens, simage is the distance from the image to the lens, f is focal length:
Thins Lens Equation:
Magnification equation with a thin lens:
So far we've assumed that light rays all focus correctly on a single point--the focus point. But sometimes light rays emanating from the same point pass through the lens or mirror and converge to different foci. This is called aberration.
There are three types of aberration in optics: speherical, chromatic,
Convex mirrors or lenses: The rays that pass through the edges of the lens focus closer to the lens than the rays that pass through the center. For instance, this lenses causes the image seen through a camera to be blurry- but using the stop mechanism of the camera, the rays that hit the edge of the lenses are blocked out, resulting in a single focus and a sharper image.
Concave mirrors or lenses: If the parallel light rays reflect from it, the rays that reflect from the center meet at one point while the rays that reflect beyond the center meet at points around the mirror's surface.
Chromatic aberration: Lenses refract light differently based on their wavelength. So as white light passes through a lenses, the individual colors (ROYGBIV-red, orange, yellow, etc.) don't focus on the same point. Violet, with a short wavelength bends more than red and focuses closer to the lens than red.
Astronomical aberration: This type of aberration, unlike the other two types, is not related to the focus of light rays. Here is an exmaple of it: From the sun, light takes about eight minutes to reach Earth and appears to travel at an angle. So the light we see is from eight minutes ago. The same phenomenon occurs with stars, except with longer lengths of time. As a result, when you are watching the stars, you are actually watching the past!