Question

Light of wavelength 600 nm passes though two slits separated by 0.25 mm and is observed on a screen 1.3 m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0.

A .At what distance, on either side of y = 0, are the m = 1 bright fringes?

B.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 ×10?16s in comparison to the wave going through the other slit. What fraction of the period of the light wave is this delay?

C. With the glass in place, what is the phase difference ??0 between the two waves as they leave the slits?

D. By how far does the central maximum move?

Answer 1

given

= 600 nm

= 600 X 10^--9 m

d = 0.25 mm

= 0.25 X 10^-3 m

L = 1.3 m

a )

the location of the bright fringe is

Y = n L / d

Y = 1 X 600 X 10^-9 X 1.3 / 0.25 X 10^-3

Y = 0.00312 m

b )

V = f

C = / T

T = / C = 600 X 10^-9 / 3 X 10⁸

T = 2 X 10^-15 sec

t = 5 X 10^-16 sec

t / T = 5 X 10^-16 / 2 X 10^-15

t / T = 0.25

c )

= 2 (t / T)

x = / 2

x = / 4

d )

the path difference r ' - ( r + / 4 )

r ' - r = / 4

r ' - r / d = y / L

y = L ( r ' - r / d )

= L / 4d

y = 1.3 X 600 X 10^-9 / 4 X 0.25 X 10^-3

y = 0.78 X 10^-3 m

y = 0.78 mm