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'n' transparent slabs of refractive index 1.5 each having thickness 1cm, 2cm, 3cm ......... n cm are arranged one over another. A point object is seen through this combination from top with perpendicular light. If the shift of the object by combination is 5cm. Then the value of 'n' is ........

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answer is A.

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Detailed Solution

Shift $= t - x; 5 = \frac{n (n + 1)}{2} - \frac{1}{1 .5} + \frac{2}{1 .5} + \dots . .$
$5 = \frac{n (n + 1)}{2} (1 - \frac{2}{3}); n^{2} + n = 30; n = 5$

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