反射と屈折

Light reflects and travels at different speeds and direction, or refracts, depending on the material through which it is propagating, causing many interesting optical phenomena.

When a ray of light strikes the surface of a glass block, a part of it changes direction at the interface to return into the medium from which it originated; this is reflection. And the rest of the light changes its direction at the interface and travels through the block of glass to conserve energy and momentum; this is refraction.

Lenses found in optical systems like microscopes make use of reflection and refraction to create images that can be perceived by the human eye.

Here, we will first discuss the principles and parameters of reflection and refraction. Then we will demonstrate these phenomena in a system where air and water are the two media. Next, we will study the ways in which lenses create images, followed by a few applications in the field of optics.

To understand the principles and parameters of reflection and refraction, let us pick two media – water and air.

The first key parameter to note is “refractive index”, ‘n’ – a characteristic of the medium through which light travels. It is defined as the ratio between the speed of light in vacuum, ‘c’, to the speed of light in the medium, ‘v’. As the n of air is lower than water, light travels more slowly through water as compared to air.

Let us now assume that the two media, water and air, are in contact with each other along an interface.

Now when light travels from water to air and hits the interface, some of it is reflected at the interface, and the remaining is refracted or bent by an angle that depends on the refractive indices of the two media. Both reflection and refraction are also dependent on another parameter – angle of incidence, or θi.

This is the angle between the incident light and the normal to the air-water interface inside the first medium, water. The ‘angle of reflection’ is measured between the reflected light and the same normal inside the first medium, water, and is equal to the angle of incidence. Whereas the ‘angle of refraction’, or θr is the angle between the refracted light and the normal to the air-water interface in the second medium, air.

The angle of refraction is thus dependent on the angle of incidence and the refractive indices of the two media. The law of refraction or Snell’s Law provides a relationship between all of these parameters.

Now, if the angle of incidence is slowly increased, at one point the light would appear along the water-air interface, and the angle of refraction will equal 90 degrees. This incident angle is called the ‘critical angle’. Note that it can only happen if the refractive index of the first medium is greater than the second one.

Under this same condition, if the angle of incidence is increased further, then the light beam is refracted so sharply that it is actually completely reflected back into the first medium from which the light originated. This phenomenon is called Total Internal Reflection.

Having reviewed the parameters that affect reflection and refraction, let’s see how to perform an experiment in a physics lab that validates these principles. Gather all the necessary materials and equipment including a specialized refraction tank with a light beam.

Fill one half of the refraction tank with water. Turn ON the light beam and direct the beam into half of the tank filled with water.

Using a protractor, measure the light beam’s angle of incidence or the angle measured in the water between the light beam and the normal to the air-water interface. Also, measure the angle of refraction or the angle measured in air between the light beam and the normal to the air-water interface

Now, as the incidence angle is increased, a point is reached at which the light beam appears along the air-water interface. Make a note of this incidence angle, as it is the critical angle for total internal reflection.

Next, continue to increase the angle of incidence by rotating the light source counter-clockwise. The refracted beam now gets completely reflected into the water demonstrating Total Internal Reflection.

Subsequently, move the light source so that the beam enters the air-half of the tank first before travelling into the water. Repeat the protocol for the new light beam path for various angles of incidence and record the corresponding angle of refraction.

Now let’s talk about lenses, which take advantage of reflection and refraction of light to create real and virtual images of objects. All lenses, whether convex or concave, have a focal length ‘f’, which is the distance from the lens at which light rays originating from infinitely far away will be focused after passing through the lens. For convex lenses f is positive and for concave lenses f is negative.

When an object is placed in front of a lens, it creates an image. The ‘Thin Lens Equation’, provides a mathematical relationship between the focal length ‘f’, the distance between the object and the lens, ‘o’, and the distance between the lens and the image, ‘i’.

It is this mathematical image distance ‘i’ that tells us whether an image formed by the lens is real or virtual. If the mathematically calculated ‘i’ is positive then the image formed will be real, and if it is negative the image will be virtual.

For a convex lens, when the object distance ‘o’ is greater than the focal length ‘f’, the mathematically calculated image distance ‘i’ will be positive and a real image is formed. This is due to the physical convergence of light rays that come from the object, like the image captured by a camera or a microscope.

However, when the object distance ‘o’ is less than the focal length ‘f’, the mathematically calculated image distance ‘i’ is negative and a virtual image is formed. This is because the light rays appear to converge but actually physically diverge, and our eyes construct a point of origin for them. This is observed in the case of a magnifying glass, where a magnified virtual image is formed.

For concave lenses, the light rays that come from the object pass through the lens and always diverge. Thus, the calculated ‘i’ is always negative and the image created is always virtual.

In this section, we will validate the formation of real and virtual images using simple convex and concave lenses. Gather the required materials, namely a convex lens, a concave lens, a sheet of white paper, a small distinctive object, and a clamp to hold the paper vertically

First, place the convex lens between the object and the piece of paper. Make sure that they are all in line and at the same height.

Move the object and paper around until a sharp image of the object appears on the paper. This image seen on the paper is a real image, as it can be captured on a screen.

Now measure the distance from the lens to the object and from the lens to the paper. Use the thin lens equation to determine the focal length of the lens.

Next, place the paper aside and move the object closer to the lens until the distance between the lens and the object is less than the focal length of the lens. Look through the lens and observe the image.

Replace the convex lens with a concave lens. Look through the concave lens and observe the demagnified virtual image.

Now that we have completed the experimental protocol, let’s review how to analyze the data obtained. In the first experiment, we measured the angle of incidence and the angle of refraction at the water-air interface.

By using the Snell’s law and substituting the values for these angles into the equation, along with the refractive index of air, we can calculate the refractive index of water, which comes out to be 1.33.

This calculation can then be repeated for the various incident and refraction angles. The average of all the calculated refractive indices will provide a more accurate measurement of the index of refraction of water.

We can also calculate the critical angle for total internal reflection using Snell’s law. This is the incidence angle when the refraction angle equals 90 degrees. Rearrange this equation to solve for critical angle.

Using the previously calculated average for the refractive index of water, Snell’s law predicts that the critical angle of incidence is 48.8 degrees. This is very close to the angle measured experimentally, thus verifying Snell’s law.

When the light beam is projected from air to water, total internal reflection does not occur even at angles greater than 48.8 degrees as light is now traveling from a medium of lower index to higher.

In the experiment with the lenses, the thin lens equation reveals that for an object distance of 11.02 centimeters from the lens and an image distance of about 9.21 centimeters, the focal length of the lens is about 5.02 centimeters.

In the case where the object is observed through a convex lens, at a distance less than its focal length, a magnified version of the object is observed. This is a virtual image, as this image cannot be captured on a screen. Similarly, when using the concave lens, a demagnified virtual image of the object is observed.

Optics, specifically optical lenses, is used in every walk of life from photography to medical imaging to the human eye.

Optical fibers are used for data transmission in many current day applications, like transmission of telephone signals. These fibers consist of a core, cladding, and a protective outer coating or buffer, and other strengthening layers.

The cladding guides the data in the form of light pulses along the core using the method of total internal reflection. This property of data transmission enables fiber optic cameras used by doctors to view confined spaces in human body.

Microscopy is the field of using microscopes to view objects that are not visible to the naked eye. Optical or light microscopy involves passing visible light, which is refracted through or reflected from the sample, through a single or multiple lenses to allow a magnified view of the sample. The resulting image can be detected directly by the eye, or captured digitally.

You’ve just watched JoVE’s introduction to reflection and refraction. You should now understand the principles of refraction, Snell’s law, and total internal reflection and also the theory behind lenses and how they create images. As always, thanks for watching!