Describe how Snell's law can be used to describe the bending of light toward and away from the normal.

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atsuzuki's profile pic

atsuzuki | (Level 1) Adjunct Educator

Posted on

What we call the bending of light is physically denominated the phenomenon of refraction of light. (In fact, not only light refracts, all waves exhibit refraction properties, but this is an aside to the question). Refraction of light may occur when it crosses transparent mediums of different refraction indices. A refraction index (the absolute refraction index) is the ratio between the speed of light in that medium as compared to the speed of light in the vacuum, namely, if we note by n the refraction index of a medium, it is given by

`n=c/v` , in which v is the speed of light in that medium and c is the speed of light in vacuum. Since c is the maximum speed possible in nature, all indices of refraction are equal or bigger than one, since v is always smaller than c. Only in vacuum the index of refraction is equal to one, although in the atmospherica air it is very close to 1.

So if we have two different mediums, say air and glass, Snell's law states that

`n_(air)*sintheta_(air)=n_(glass)*sin theta_(glass)` where the angles `theta_(air) and theta_(glass)` are measured with respect to the normal (line that is perpendicular to the surface of separation between air and glass.)

Now, suppose the light coming from the air strikes the glass perpendicularly, that is to say, `theta_(air) = 0^0` . Since `sin 0^0 = 0` it follows that in this case `theta_(glass)=0^0`  also. In this case, there is NO bending of light as it passes from air to glass. However, if the light coming from the air strikes the glass forming an angle say `theta_(air) = 30^0` and using the fact that sin of 30 degrees is 1/2, we have the following result:

`sintheta_(glass)=(n_(air))/(2*n_(glass))~= 1/(2*n_(glass))`

Now, because the index of refraction of glass is greater than 1 (about 1.7) it means that

`sintheta_(glass)<0.5` . This means that `theta_(glass) < 30^0` or that light, as it enter the glass, bends toward the direction of the normal line. 

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

Snell's law describes how the direction of the rays of light changes when the light falls on the surface between two different media, for example, air and water.

The direction of the rays of light is described by the angle between the ray and the normal to the surface. The angle at which light falls on the surface in the first medium is called the angle of incidence (`theta_i` ), and the angle at which the light enters the second medium is called the angle of refraction (`theta_r` ).

The Snell's law says that the relationship between the two angles is

`(sin(theta_i))/(sin(theta_r)) = n_2/n_1` ,

where n_1 and n_2 are the the indices of refraction for the first and second medium, respectively. These numbers describe the electromagnetic properties of the media.

Please see the reference website (linked to below) for more information.

Sources:

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