Answer:
the angle of the prism = 30 degrees
Explanation:
The angle of minimum deviation for a prism =
[tex]\mu =(\frac{{sin(A+dm)}/{2}}{sin A/2})[/tex]
for an equilateral prism, A=60∘
This gives us
[tex]1.414 =(\frac{{sin(60+dm}/{2)}}{sin(60/2)})\\1.414 =(\frac{{sin(60+dm}/{2)}}{0.5})\\0.707 = sin {(60 +dm)/2}\\[/tex]
taking the Arcsin of both sides we have
[tex]45 =\frac{60+dm}{2}\\90 = 60+dm\\dm = 30 degrees[/tex]
Recall that the angle of the prism is equal to the angle of minimum deviation.
Hence, the angle of the prism = 30 degrees
