Probenoflgh that consists of a mixture of red, green and violet light strikes a

Question

Probenoflgh that consists of a mixture of red, green and violet light strikes a prism urounded by air) as shown. Indices of refraction for this prism for the various colors are shown in the table. An observer is located to the right of the prism as shown. Which colors) A beam could, in principle, be seen by the observer? color violet green red 1.43 1.40 1.37 Incident bearn 45 (A) only red light (B) only green light (C) only violet light (D) only green and red light (E) only green and violet light

Explanation / Answer

Ans: (E) Only green and violet light.

Snells law: n1sin1 = n2sin2

To find 2 (angle at which light exits) you manipulate

n1 (red) = 1.43

(green) = 1.40

(violet) = 1.37

n2 (air) = 1

1 = 45 degrees

sin2 = n1sin1/n2

2 = sin^-1 n1sin1/n2

2 (red) = sin^-1 1.43sin45/1 = ERROR (Total Internal Reflection)

Crit. Angle for red = sin^-1 (n2/n1) = sin^-1 (1/1.43) = 44.4 degrees

Incident ray is 45 degree (greater than Crit angle) causing red to COMPLETELY reflect instead of refracting into viewers eyes

2 (green) = sin^-1 1.40sin45/1= 81.87 degree

2 (violet) = sin^-1 1.37sin45/1 = 75.64 degree

Theoretically the viewer can only see green and violet as red would reflect

[However, if the viewer looked to side of the prism, he can see the reflected red ray]

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