A ray of light travelling from glass to air is incident at 50 degree from the glass air boundary. What is angle of deviation if the critical angle is 42 degree
the angle of incidence frm the normal is 40 deg
Use Snelll's law.
To find the angle of deviation in this scenario, we need to understand a few concepts in optics.
1. Angle of Incidence (i): This is the angle at which the incoming ray strikes the boundary between the two media. In this case, it is 50 degrees.
2. Angle of Refraction (r): This is the angle at which the ray bends when it enters the second medium. It follows the law of refraction, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.
3. Critical Angle (C): This is the angle at which the light ray is incident on the boundary and gets refracted along the boundary instead of passing through it. It is determined by the refractive index of the two media.
Now, let's calculate the angle of refraction using the formula for the law of refraction:
sin(i) / sin(r) = refractive index of air / refractive index of glass
Or, sin(50) / sin(r) = 1 / refractive index of glass
Now, we know that when the angle of incidence is greater than the critical angle, total internal reflection occurs. In this case, since the angle of incidence (50 degrees) is less than the critical angle (42 degrees), the light ray will be refracted and not undergo total internal reflection.
So, we can use the formula for refraction to calculate the angle of refraction:
sin(i) / sin(r) = refractive index of air / refractive index of glass
Using the values for the refractive indices of air and glass (approximately 1 and 1.5, respectively):
sin(50) / sin(r) = 1 / 1.5
Now, we can solve this equation for sin(r):
sin(r) = sin(50) / 1.5
r = arcsin(sin(50) / 1.5)
Evaluating this expression using a scientific calculator, we find that r is approximately 34.41 degrees.
Now, to find the angle of deviation, we can use the formula:
Angle of Deviation = Angle of Refraction - Angle of Incidence
Angle of Deviation = 34.41 - 50
Angle of Deviation ≈ -15.59 degrees
Therefore, the angle of deviation in this case is approximately -15.59 degrees.