glass block whose refractive index
is 1.564 for sodium light is to be
used to construct a prism such that
the angle of minimum deviation for
such light shall be equal to the angle
of the prism. What is the angle of
the prism?
Given that the refractive index of the glass block is 1.564 for sodium light, we can use Snell's Law to calculate the angle of minimum deviation for the prism:
n1*sin(angle of incidence) = n2*sin(angle of refraction)
Where n1 is the refractive index of air (approximately 1) and n2 is the refractive index of the glass block (1.564).
Therefore, sin(angle of incidence) = n2*sin(angle of refraction)
Let's denote the angle of minimum deviation as D.
sin(D) = 1.564*sin(D/2)
Now, we can solve for D using this equation:
1.564*sin(D/2) = sin(D)
1.564*2*sin(D/2)*cos(D/2) = 2*sin(D)*cos(D/2)
1.564*cos(D/2) = 2*cos(D/2)
1.564 = 2
D/2 = arccos(1.564/2)
D/2 = arccos(0.782)
D = 2*arccos(0.782)
D ≈ 78.3 degrees
Therefore, the angle of the prism is approximately 78.3 degrees.