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.
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?
1 answer