Question

Use snell's law to find the refractive index of liquid with respect to air

Answer 1

bend. This law is more complicated than that for reflection, but an understanding of refraction will be necessary for our future discussion of lenses and their applications. The law of refraction is also known as Snell's Law, named for Willobrord Snell, who discovered the law in 1621.

Snell's Law

Like with reflection, refraction also involves the angles that the incident ray and the refracted ray make with the normal to the surface at the point of refraction. Unlike reflection, refraction also depends on the media through which the light rays are travelling. This dependence is made explicit in Snell's Law via refractive indices, numbers which are constant for given media1.

Snell's Law is given in the following diagram.

Basic illustration of Snell's Law.

As in reflection, we measure the angles from the normal to the surface, at the point of contact. The constants n are the indices of refraction for the corresponding media.

Tables of refractive indices for many substances have been compiled.

n for Light of Wavelength 600 nm

Substance Refractive Index, n

Air (1 atmosphere pressure, 0 degrees C) 1.00029

Water (20 degrees C) 1.33

Crown Glass 1.52

Flint Glass 1.66

Say, in our simple example above, that we shine a light of wavelength 600 nm from water into air, so that it makes a 30o angle with the normal of the boundary. Suppose we wish to find the angle x that the outgoing ray makes with the boundary. Then, Snell's Law gives

1.33 sin 30o = 1.00029 sin x

x = 41o

Refraction certainly explains why fishing with a rod is a sport, while fishing with a spear is not2.

A more complicated illustration of Snell's Law proves something that seems intuitively correct, but is not obvious directly. If you stand behind a window made of uniform glass, then you know by now that the images of the things on the other side of the window have been refracted. Assuming that the air on both sides of your window have the same refractive indices, we have the following situation:

Two refractions.