(10%) Problem 8: Suppose you are using total internal reflection to make an effi

Question

(10%) Problem 8: Suppose you are using total internal reflection to make an efficient corner reflector that is, a Prism material shaped so that the light is reflected back towards its source. For example, each one of the prisms in the binocular shown is a corner reflector Randomized Variables Prism Light ray Otheexpertta.co p à If there is air outside and the incident angle at the first glass-air interface is 39° with respect to the normal, what must be the minimum index of refraction, "min of the material from which the reflector is made, to ensure that total internal refraction occurs at the first interface? Grade Summary Deductions Potential emin sinO cotan) asin coso tanO acoso Submissions Attempts remainin 4 per attempt) detailed view tn acotan sin0 cosh tan cotanh0 Degrees O Radians 0 I give up! s: 4% deduction per hint. Hints remaining: Feedback: 5 deduction per feedback

Explanation / Answer

for Total internal reflection,

Using snell's law:

n1*sin A1 = n2*sin A2

when TIR, A2 = 90 deg

sin A2 = 1,

& A1 = Critical angle = Ac

n1*sin Ac = n2

Given that Ac = 39 deg

n1 = refractive index for air = 1

So,

n1 = n2/sin Ac

n1 = 1.00/sin 39 deg

n1 = 1.589

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