The critical angle of glass is 41degree 48 seconds and that of water is 48 degree 36 seconds.calculate critical angle of the glass water interface?
Ans
To calculate the critical angle of the glass-water interface, you need to first determine the refractive index of both glass and water using their respective critical angles. The refractive index, also known as the index of refraction, is the ratio of the speed of light in a vacuum to the speed of light in a medium.
The formula to calculate the refractive index (n) is:
n = 1 / sin(C)
Where C is the critical angle in radians. However, since the critical angles are given in degrees and seconds, we need to convert them to decimal degrees before using the formula.
Converting the critical angle of glass:
41 degrees 48 seconds = 41.8 degrees
Converting the critical angle of water:
48 degrees 36 seconds = 48.6 degrees
Now, we can calculate the refractive indices:
For glass:
n(glass) = 1 / sin(41.8 degrees)
For water:
n(water) = 1 / sin(48.6 degrees)
Now, to find the critical angle of the glass-water interface, we will use the formula:
C(interface) = arcsin(n(glass) / n(water))
Substituting the values:
C(interface) = arcsin(n(glass) / n(water))
= arcsin((1 / sin(41.8 degrees)) / (1 / sin(48.6 degrees)))
Using a scientific calculator or an online calculator to find the arcsin of the calculated ratio will give you the value of the critical angle for the glass-water interface.