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A parallel beam of light of wavelength greater than 3500 Å falls on a double slit in a Young’s double slit experiment. It is found that wavelengths 4000 Å and 6000 Å produce maxima simultaneously at a distance of 32mm from the position of central maximum and the order of the interference at this point for the two wavelengths differs by 8. If the distance between the slit and the screen is 1m, the separation between the two slits is

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0.2mm

0.3mm

0.12mm

0.18mm

answer is B.

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Detailed Solution

if both maxima are produced simultaneously and their order no differs by eight then n x 6000 = (n+8) 4000 n=16

hence position of 16 th maxima of 6000 $\overset{0}{A}$ i.e 16 $β$ from the central maxima $(β = \frac{λ D}{d})$

$16 \frac{6 \times 10^{- 7} D}{d} = 32 \times 10^{- 3} d = 3 \times 10^{- 4} m = 0.3 m m$

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