Spherical Mirror Optics
From MyMCAT
Contents |
Introduction
This page is part II to optics on the MCAT, refer back to Optics Introduction for the previous page.
Images
To perceive an image, your mind traces back along the path of the light rays that enter your eye and deduces the object based on the assumption that light rays travel in straight lines. Reasoning and visual cues may be used to recognize that the objects seen are not real, but rather reflections, but without this extra information, one cannot determine whether an object is really infront of you or simply an image of an object projected by some other means.
Two common methods of altering images is by means of mirrors and lens. Spherical mirrors can be concave or convex and lens can be converging or diverging.
Spherical Mirrors
When light comes off an object and hits a mirror it will reflect back. However, because of the curvature of a spherical mirror, each ray of light will be reflected back at a slightly different angle, resulting in the reflected rays converging in the case of a concave mirror or diverging in the case of a convex mirror. (One can remember which way the mirror reflects by imagining the mirror sideways and pouring water onto it. If the water pools in the center, it is converging it, but if the water runs off either side, it is diverging it.)
When horizontal rays of light reflect on a concave mirror, the reflected rays will focus onto a single point called the focal point. In the case of a convex mirror, the reflected rays will all diverge outwards, but if one traces backwards along the path of each ray, there will also be an equivalent focal point on the other side of the mirror. In both cases, the focal point is found on the side of the inward curvature, which also happens to be exactly 1/2 of the radius curvature of the mirror.
(image: horizontal rays focusing on focal point on concave and convex mirrors)
Ray Diagrams
Ray diagrams are used to help understand how light hitting a concave mirror (or lens) behaves. Understanding the path of photons before and after they hit can help answer many problems, however keep in mind that drawing is NOT on the MCAT, and therefore this tool is purely for grasping the mathematics that will follow. Here are three basic rules to use when tracing rays:
- horizontal rays which hit the mirror (or lens) will always reflect (or refracts) through the focal point
- rays which move directly through the focal point will then reflect (or refract) to become horizontal (this is just the previous rule in reverse since the angles are all the same!)
- a ray which strikes the exact middle will reflect back (or refract) at the exact same angle it entered with (this is just like angle of incidence equals angle of refraction)
(image: tracing the three rays on a concave and convex mirror)
Magnification
A mirror (or lens) may or may not magnify the size of image (versus the size of the object). The magnification can be determined by the ratio of the height of the image to the height of the object. It can also be determined however by the negative of the distance of the image to the mirror compared to the distance of the object to the mirror.
If the absolute value of the magnification is greater than one, the image is larger than the original object, if it is equal to 1, it is the same size, and if it is less than one, the image is smaller than the original. If the magnification is negative, the same rules apply however the image will be inverted (or flipped upside down).
The Thin Lens Equation
Now that we understand the basics of ray tracing and magnification, a simple formula can be used to determine where an image will be represented based on the focal point and the original object for mirrors and lens.
To correctly solve mirror and lens problems, one must be sure to assign the correct signs to each value.
