Question

Monochromatic light falls on two very narrow slits 0.049 mm apart. Successive fringes on a screen 6.70 m away are 8.2 cm apart near the center of the pattern.

Part A Determine the wavelength of the light. Express your answer to two significant figures and include the appropriate units Part B Submit Request Answer Determine the frequency of the light. Express your answer to two significant figures and include the appropriate units

Answer 1

for constructive interference in two slit experiment we know that

m* = d*sin

for small angles we know that

sin = = tan = y/D

So,

m* = d*y/D

y1 = m**D/d

y2 = (m + 1)**D/d

So,

y2 - y1 = (m + 1)**D/d - m**D/d

y2 - y1 = 1**D/d

= d*(y2 - y1)/D

Given values are:

D = distance between screen-slit = 6.70 m

d = distance between two slits = 0.049 mm = 0.049*10^-3 m

y2 - y1 = distance between to successive fringes = 8.2 cm = 0.082 m

So,

= 0.049*10^-3*0.082/6.70

= 5.997*10^-7 m = 599.7*10^-9 m

In two significant figures:

= 600*10^-9 m = 600 nm

Part B.

frequency = c/

c = speed of light = 3*10^8 m/sec

f = 3*10^8/(600*10^-9)

f = 5.0*10^14 Hz

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