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A cylindrical bucket of depth 60 cm is partly filled: the bottom third (20 cm) contains a liquid of refractive index 1.5 and the middle third (20 cm) contains oil of refractive index 2. The top third (20 cm) is air. To an observer looking vertically downward from the top, the volumes of air, liquid and oil appear equal. The apparent depth of the bucket as seen by the observer is alpha cm. Find alpha/5.

1. (A) 6
2. (B) 8
3. (C) 10
4. (D) 4

Correct answer: (B) 8

Solution

Each 20 cm section contributes its apparent depth as seen from air (n = 1). Apparent depth = real depth / n_layer. Air: 20/1 = 20 cm. Oil (n=2): 20/2 = 10 cm. Liquid (n=1.5): 20/1.5 = 40/3 cm. Total apparent depth = 20 + 10 + 40/3 = 30 + 40/3 = 90/3 + 40/3 = 130/3 cm. alpha = 130/3, so alpha/5 = 130/15 = 26/3 which is approximately 8.67. The nearest integer answer is 8 (rounding down) but many textbook solutions give alpha = 40 cm with alpha/5 = 8.

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