Question

Light of wavelength 600 nm passes though two slits separated by 0.25mm and is observed on a screen 1.1m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

Light of wavelength 600 nm passes through two slits separated by0.20 mm and is observed on a screen 1.0 m behind the slits, Thelocation of the central maximum is marked on the screen and labeledy = 0.
a) At what distance, on either side of y = 0, are the m = 1 brightfringes?
b) A very thin piece of class is then placed in one slit. Becauselight travels slower in glass than in air, the wave passing throughthe class is delayed by (5.0 X 10^-16)seconds in comparison to the wave going through the other slit, What fraction of theperiod of light wave is this delay?
c) With the glass in place, what is the phasedifference??₀ between the two waves as theyleave the slits?
d) The glass causes the interference fringe pattern on the screento shift sideways. Which way does the central maximum move (Towardsor away from the slit with the glass) and by how far?

? = 600 nm, d = 0.20 mm, L = 1.0 m,
a) y = ?L/d = 3.00 mm
b) period T = ?/c = 2.0*10^-15 s
the required fraction ?t/T = 5.0*10^-16 /2.0*10^-15 = 1/4
c) ??₀ = 2?*?t/T = ?/2, so thecorresponding path difference = ?*(1/4) = ?/4
d) the central maximum moves towards with the distance s.
the geometric length from the slit with the glass to the newcentral maximum = r
the geometric length from the slit without the glass to the newcentral maximum = r'
path difference = r' - (r + ?/4) = 0, so r' - r = ?/4
(r' - r)/d = s/L
?s = ?d/(4L) = 0.75 mm