4 1pt Light travelling through air n 100 enters an optical

4. [1pt]
Light travelling through air (n = 1.00) enters an optical fibre (n = 1.10); the light is refracted and reflected as shown in the figure. If the angle of incidence is ₁ = 50.0°, what is the angle ₂ at which the light exits the side of the optical fibre (following the path labelled A)?

Answer:  

Solution

The incident ray undergoes two refractions at the top surface and the left surface respectively.

For first refraction, using Snell\'s law,

1 x sin (₁) = 1.1 x sin (₁^\')

i.e. 1 x sin (50^o) = 1.1 x sin (₁^\')

or, ₁^\' = 44.1^o

For second refraction,

1.1 x sin (₁^\'\') = 1 x sin (₂)

where, ₁^\'\' is the incident angle for second (left) surface and is given by:

₁^\'\' = 90^o - ₁^\' = 45.9^o

Substituting,

1.1 x sin (45.9^o) = 1 x sin (₂)

or, ₂ = 52.2^o