What is the value of critical angle for the diamond-air interface (refractive index of diamond is 2.42)?
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A.
47°
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B.
25.6°
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C.
24.4°
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D.
90°
Correct Answer:
C. 24.4°
Explanation:
The critical angle for a diamond-air interface, where the diamond has a refractive index of 2.42, is approximately 24.4°.
This value is determined using the formula for the critical angle: θc = arcsin(n2 / n1). In this scenario, n1 represents the refractive index of the denser medium (diamond, 2.42) and n2 represents the refractive index of the rarer medium (air, approximately 1.00). By calculating arcsin(1 / 2.42), the result is approximately 24.4°. This small critical angle is a key factor in the brilliance of diamonds, as it increases the likelihood of total internal reflection, trapping light within the stone and causing it to sparkle.
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