Optics Introduction

From MyMCAT

Introduction

Geometric optics is the physics which deals with rays of light. How light behaves when it hits a flat mirror, a curved mirror, or goes through a lens are all examined in this section. Geometric optics questions on the MCAT are often very simple, however these questions often cause the most difficulty due to the vexing matter of sign conventions in lens and mirror calculations.

Reflection from a plane surface

The law of reflection of light is merely that the angle of reflection r is equal to the angle of incidence r. The diagram below easily demonstrates this concept.

In general, the angles of incidence and reflection are measured from from the normal to the reflecting surface rather than from the surface itself. When we see our reflection in the mirror, we ourselves are considered a "real object" and the reflection which "looks" like it is in front of us but beyond the mirror is considered a "virtual image" (because it is virtual and not really there). Furthermore, the image in a mirror is reversed from left to right, and from back to front, but is not reversed up and down. When we are dealing with distances and angles, if one moves the mirror a distance d away from the observer, the virtual image appears to move a distance 2d. For the same reasoning, if the mirror rotates an angle x, the virtual image will rotate 2x.

Refraction

Have you ever looked down at a pool on a sunny day and noticed that you could see a reflection of yourself and the bottom of the pool at the same time? This phenomena is a result of partially reflective surfaces and while the rays which undergo reflection are governed by the law of reflection, the rays which enter the water behave differently. When a ray of light enters a denser medium (like water) it is refracted towards the normal in such a manner than the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, this constant being called the refractive index n. Many different mediums can be experimentally examined to determine their refractive indexes, but in the case of the MCAT these values will be given to you should you need them.

The incident and refracted rays are on opposite sides of the normal at the point of incidence. In general, the change in angle (and direction of light) before and after is described by Snell's Law,

$n_1\sin\theta_1 = n_2\sin\theta_2$

When light enters a denser medium (ie from the air to water, or from a vacuum to a crystal) the angle is always reduced, when light exits a dense medium to a lighter medium the angle is always increased (this can be seen if one tries various values for n1 and n2 in Snell's formula). While generally the values of n are given, they can also be calculated either by knowing the angles before and after, or knowing the speed of light in the medium of question. The absolute index of refraction for a given medium is defined as: n = c/v where c is the speed of light in a vacuum and v is the speed of light in the medium.

Total Internal Reflection

An effect of total internal reflection combines both refraction and reflection and conceptually can be difficult to understand, but visually quite straight forward. Consider light coming from a dense medium like water into a less dense medium like air. When the light coming from the water strikes the surface, part will be reflected and part will be refracted. Measured with respect to the normal line perpendicular to the water surface, the reflected light comes off at an angle equal to that at which it entered at (reflection), while that for the refracted light is larger than the incident angle (because of snell's law of going from a dense to lighter medium). In fact the greater the incident angle, the more the refracted light bends away from the normal. Thus, increasing the angle of incidence will eventually reach a point where the refracted angle is 90 degrees, at which point the light appears to emerge along the surface between the water and air. If the angle of incidence is increased further still, the refracted light cannot leave the water and instead is completely reflected. The interesting thing about total internal reflection is that it really is total. That is 100% of the light gets reflected back into the more dense medium, as long as the angle at which it is incident to the surface is large enough.

Because the critical point occurs when the sine from the normal line to the surface reaches 90 degrees, we can use snell's law to determine the necessary conditions for total internal reflection for any medium. Specifically,

$\frac{n_1}{n_2} = \frac{\sin\theta_2}{\sin\theta_1} = \frac{\sin 90}{\sin\theta_2} = \frac{ 1 }{\sin\theta_1}$

Therefore, the sine of the critical angle to achieve total internal reflection is equal to the ratio n2/n1, where n1 is the denser medium (n1>n2) that the light was trying to exit from (but got reflected back).

$\sin \left( \theta_{critical} \right) = \frac{n_2}{n_1}$

Dispersion

Dispersion is the phenomenon in which a spatial separation of a white light into its component wavelengths (colours) occurs. Media having such a property are termed dispersive media. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature and the most classical example of this effect is sunlight dispersing into a rainbow when it passes through a prism (or raindrops to form rainbows in the sky).

Next Section

Now that we have an introduction in the basic concepts of reflection, refraction, and dispersion, proceed to the next section, Spherical Mirror Optics for a continuation of the geometric optics section.