A twin slit apparatus has narrow slits separated by 0.800 mm. It is illuminated

Question

A twin slit apparatus has narrow slits separated by 0.800 mm. It is illuminated by light from a white light source, which has passed through a narrow-band filter (passband width ??, centre wavelength 450 nm) and then through a single narrow slit, before reaching the double slit apparatus. The light passing through the twin slits falls on a distant screen. It is observed that clear bright and dark fringes are seen on the screen near the axis, but that the contrast of the fringes fades out at 1.2? from the axis, even though there is still some light reaching the screen there.

(i) Calculate the coherence length of the light passing through the twin slit system.

I'm not really sure how to go about it, the formula from for coherence length is l=?^2 / ??. However the ?? is unknown.

Explanation / Answer

the fringe width is B = lamda * D/d where lamda = 450 nm = 450 * 10^-9 m,D = 1 m and d = 0.800 mm = 0.800 * 10^-3 m the coherence length is L = B * sinA where A = 1.2o

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