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A light ray is incident normally to the long face (the hypotenuse) of a $45^{\circ}-45^{\circ}-90^{\circ}$ prism surrounded by air, as shown in Figure 22.26b. Calculate the minimum index of refraction of the prism for which the ray will totally internally reflect at each of the two sides making the right angle.

$\begin{array}{l}{\text { Thus the minimum index of refraction of the prism for which the ray will }} \\ {\text { totally internally reflect at each of the two sides making the right angle is }} \\ {n=1.414 \text { . }}\end{array}$

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Cornell University

Numerade Educator

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Hope College

we have following situation Prism prism Here, Uh, with 2 45 degrees here, 45 45 degree. This is a 90 degree life, strikes at the inside and then, uh, transmits here. Then it reflects totally internally. And then it goes out of this site. Um, so if you bisect this and we only have 45 year 40 45 year here, 45 you draw a normal here again, we have 45 here and then here we have 25. This one is a 45. For a total internal reflection, the critical angle should be less less than or equal to 45 degrees so that the incident Ray can be totally entering reflect the condition for total internal reflection we know is signed that are critical angle is 1/4. And to divide by anyone where and one is greater than in two and one in into a refractive indexes. And do we have is one that we can solve for ah, end. So in will be one we're sign. They don't see ah securing value for critical angle, which is Ah, signed 45. This gives us a refractor index off 1.414 The minimum index offer fraction for the prison for reaching the rage should be totally reflected. Each off the two sides. Making the right angle is a musical to 1.414