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 95 dark fringes. Calculate the number of dark fringes that appear if water (n = 1.33) replaces the air between the plates.

Explanation / Answer

condition for destructive interference; phase difference(p)= (m+1/2)*L; L-wavelength

pathe differnce(d)= 2nt + L/2 ;{because there is a pi phase shift due to relection by the bottom glass surface

(m+1/2)*L = 2nt + L/2

2nt= mL ; so for air maximum t= 95*L/2 {n=1 for air}

for maximum t when water is filled, 2*1.33*[95*L/2] = m*L;

m=126.35 ; since m is an integer

number of dark fringes that appear (m)=126

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