Many cells are transparent and colorless. Structures of great interest in biolog

Question

Many cells are transparent and colorless. Structures of great interest in biology and medicine can be practically invisible to ordinary microscopy. An inference microscope reveals a difference in refractive index as a shift in inference fringes, to indicate the size and shape of cell structures. The idea is exemplified in the following problem. An air wedge is formed between two glass plates in contact along one edge and slightly separated at the opposite edge. When the plates are illuminated with monochromatic light from above, the reflected light has 89 dark fringes. Calculate the number of dark fringes that appear if water (n = 1.33) replaces the air between the plates. 1

Explanation / Answer

Here we have the condition for destructive interference forthese reflected waves is    2nfilmt = m or 2t = m /2nfilm for air film nfilm = 1.0 the maximum thickness of the film is     tmax = m/2nfilm given total of 89 dark fringes are appeared i.eby counting them = 0 order from the edge of contact. so for maximum thicknesshighest order dark band is m = 88 so tmax = 88 /2*1.0         = 44 for water film , we have mmax = 2tmax(nfilm/)           =2*44*1.33 /           =117 therefore the total number of dark fringes that will appear ifair between the plates is replaced by water from counting thezeroth order dark fringe will be 118.

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