The path of every light ray could be reversed. In other words, the path of a light ray will be the same whether it is going forward or backward. Look, then, at what happens if you shine a flashlight up from the bottom of a swimming pool:

Notice that there is a ray which exits and just skims the surface. What would happen if another ray came in at an even narrower angle to the surface? Obviously it can't skim the surface after it exits, that would be duplicating a path already called for. The ray will be reflected! In fact, it will be 100% reflected, better than the best mirror humans can make. The angle at which this reflection occurs is called the critical angle.

21. Find the critical angle for water.

The critical angle is where the exit ray just skims the surface: 1.33sinØ = (1)sin90 sinØ = 1/1.33 Ø = 48.8°

22. An oil spill has covered a lake with oil of unknown index of refraction. It is observed, however, that the critical angle between water and oil is 71°. What, then, is the index of refraction of the oil?

At exactly Øc, a ray skims the oil-water interface. Thus: nsin90 = 1.33sin71 n = 1.26

23. A block of plastic with n = 1.3 receives a light ray as shown. What is the angle Ø which will result in the internal reflection shown?

1.3sinØc = (1)sin90 Øc = 50.3° 90 - Øc = 39.7° (1)sinØ = 1.3sin39.7 Ø = 56.1°

One of the devices that uses the principle of refraction is the lens. By curving the two lens surfaces in different ways, light may be forced to converge or diverge, as desired. Study the pictures below, keeping in mind how light should be bent as it strikes each surface.

a)

b)

c)

Lens A, a convex lens, will force light to undergo two refractions toward the axis of the lens. Lens B is similar, but its thin, gentle curvature results in a longer focal length than in lens A. Lens C, a concave lens, causes a divergence of light away from the axis.

24. Determine what reflective or refractive element will produce the light paths shown.

a)	b)	c)
d)	e)	f)
g)	h)

a)	b)	c)	d)
e)	f)	g)	h)

Notice how an object closer to the lens will form an image:

Any ray passing parallel to the axis of the lens will leave by going through the focal point (see ray A). Any ray passing through the focal point will leave parallel to the axis (see ray B).

Obviously, an object actually located on the axis will form an image on the axis, so we draw the diagram above like this:

25. Sketch these on another piece of paper and find the location of each image.

a)	b)
a) note: this is how a slide projector works	b) note: the image created is called a "virtual image." It can't be projected on a screen, but it can be seen by an eye looking through the lens. This is how a magnifying glass works

For a diverging lens (one thinner at the center than the edge), any ray coming in parallel to the axis will leave as if it had come from the focal point on the opposite side of the lens (see ray A). Similarly, any ray heading for the focal point on the opposite side will exit parallel to the axis.

26. Trace these on another sheet of paper and locate the images.

a)	b)
a) A small virtual image is formed, making this a demagnifying glass	b) A small virtual image is formed. This process is similar to that witnessed by looking into the back of a spoon.