A prism of glass of index of refraction 1.50 has angle of 45,45,90. A ray of light is incident on one of the short faces at an angle of theta. What is the maximum value of theta for which the ray of light suffer total internal reflection at the long face?
i know that the two angles inside the prism are sum to 45 degrees.
n(air)sin(theta)=n(glass)sin(b)
and
n(glass)sin(c)=n(air)sin(90)-for reflection
also
b+c=45
not sure how to continue....
sin(theta)=cos(b)-sqrt(2)
but its not a final answer
To find the maximum value of theta for which the ray of light suffers total internal reflection at the long face of the prism, we need to consider the critical angle.
The critical angle is the angle of incidence at which the refracted ray is at an angle of 90 degrees with respect to the normal. Beyond this angle, total internal reflection occurs.
First, let's find the critical angle for the glass prism. We can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction.
The index of refraction of the air is approximately 1.00, and since the angle of incidence is measured with respect to the normal, we can calculate the critical angle using the formula:
sin(critical angle) = 1 / index of refraction
Substituting the values, we get:
sin(critical angle) = 1 / 1.50
Now, we can solve for the critical angle:
critical angle = arcsin(1 / 1.50)
Using a calculator, we find that the critical angle is approximately 41.81 degrees.
Therefore, the maximum value of theta for which the ray of light suffers total internal reflection at the long face of the prism is 41.81 degrees. Any angle greater than this will result in total internal reflection.