Sample Problems for Snell's Law

Important Information

Snell's Law describes how light bends when traveling from one medium to the next.  Mathematically, it is stated as
 
n1 sin θ1= n2 sin θ2.

where ni represents the index of refraction in medium i, and θi represents the angle the light makes with the normal in medium i.

Sample Problem 1:

Light travels from air into an optical fiber with an index of refraction of 1.44.  (a)  In which direction does the light bend?  (b)  If the angle of incidence on the end of the fiber is 22o, what is the angle of refraction inside the fiber?  (c)  Sketch the path of light as it changes media.

Solution:

 
(a) Since the light is traveling from a rarer region (lower n) to a denser region (higher n), it will bend toward the normal.
(b) We will identify air as medium 1 and the fiber as medium 2.  Thus, n1 = 1.00, n2 = 1.44, and θ/font>1 = 22o.  Snell's Law then becomes
(1.00) sin 22o = 1.44 sin θ2.
sin θ2 = (1.00/1.44) sin 22o = 0.260
θ2 = sin-1 (0.260) = 15o.
(c) The path of the light is shown in the figure below.

Sample Problem 2:

Light traveling through an optical fiber (n=1.44) reaches the end of the fiber and exits into air.  (a)  If the angle of incidence on the end of the fiber is 30o, what is the angle of refraction outside the fiber?  (b)  How would your answer be different if the angle of incidence were 50o?

Solution:

(a) Since the light is now traveling from the fiber into air, we will call the fiber material 1 and air material 2.  Thus, n1 = 1.44, n2 = 1.00, and θ1 = 30o.  Snell's Law then becomes
(1.44) sin 30o = 1.00 sin θ2.
sin θ2 = (1.44/1.00) sin 30o = 1.44 (0.500) = 0.720
θ2 = sin-1 (0.720) = 46o.
Notice that this time, the angle of refraction is larger than the angle of incidence.  The light is bending away from the normal as it enters a rarer material.
(b) Replacing the angle of incidence with 50o gives
sin θ2 = (1.44/1.00) sin 50o = 1.44 (0.766) = 1.103
This equality cannot be met, so light cannot exit the fiber under these conditions.

The situation in part (b) is an example of total internal reflection, discussed on the next content page.
 
 

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