Question

Colors observed in certain fish scales are due to thin film interference. Assume that a fish scale is a translucent wedge having an index of refraction of n=1.2 and it is situated in water, n=1.45. When illuminated with white light, several complete spectra are observed.
A. What is the minimum thickness of the scale at the first red spot (l=699nm)? Repeat for the 2^nd, 3^rd, and 4^th spot. We will call these “orders”.
B. What is the minimum thickness at the blue spot (l=375nm)? Repeat for the 2^nd, 3^rd, and 4^th order blue spot.
C. Organize your information from part A and B in a list by increasing thickness. At each thickness indicated the color and order number.
D. Look at this pattern. You may have to extrapolate. Is there a thickness/order at which a blue spot overlaps a red spot from a previous order?
E. If the maximum thickness of the wedge is 3500nm at the thickest edge, how many complete spectra can we see

Answer 1

Answer- Given that na 2 1.2 ,n,= 1.45 a 2 red 699 nm blue 375 nm m=1,2,3, u we know 21= (m+5) 1:(m+?) 2 2n2 mal · La 3 x 699 2x 1-2 -436.875 nm m.2, L = 699 X 2 = 728.125 nm 2X 1.2 m-3 7 La x 699 1099.375 nm 2x 1.2 u, L=9 699 1310-625 nm 2x 1.2 b) mal, ( 3 375 2 x 1.2 = 234.375 nm m=2 La 5 375 2 . 390.625 nm 2 x 1.2 m3, L = 7 375 2 546.875 nm 2x1.2 mau L = 9 375 2 T03.125 nm 2x 1.2

2 (Candd) Red 436.875, m-1 Blue 234.375 728.1256 2 390.625 1019.375 3 546.875 1310.625 703.125 the values in the table when a thickness /order at blue spot overlaps a red spot: are shocon cwhich a L=3500 nm 2X 3500 699 1.2 (m+) (m+5) 15 2X 3500 m.22.4 23 There will 12 complete spectra for red and 23 complete Spectra for blue colour.