Question

a. Give the derivation for the condition for two-slit interference. Make sure you use

words and a diagram to communicate the derivation.

b. Based on previous measurements, the lines are at 589.592 nm and 588.995

nm. The diffraction grating is the same one you used in class, 600 lines per millimeter.

You shine it on an inexpensive camera like the one in your phone where the pixels are 1.7

nm apart. To make your measurement, you want to choose the distance to the camera

such that these two lines are ten pixels apart. If you do this, and use the known sodium

light calibrate everything well, you will have engineered your device to measure

wavelengths with 0.01% or 0.05 nm precision. Is the distance reasonable ?

c. How much further does the xray bounding off the lower layer need to go, compared to

the upper layer ? If you see constructive interference at 14.3 degrees and the X-rays have

a wavelength of 0.16 nm, what is the spacing between these atomic layers within the

crystal?

Answer 1

slits s1 and s2 are illuminated by a monochromatic source of light. The two slits act as source of light and they are coherent sources.

Light waves from s1 and s2 meet at a point P. on a screen at a distance D

Path difference between the two rays difference by a distance dSin

The two wave meeting at P will constructively interfere and produce a bright spot if the path difference between the two is an integral multiple of

dSin = n ( n = 0, +/-1, +/-2 , .... )

for n=0 , the path difference is 0 and there will be bright spot , where P is on a line through the center of both slits.

for small angles w can approximate Sin = Tan = y/D

for y = nD/d , we have bright fringes on the screen

b)

₁ = 589.522 nm ;  ₂ = 588.995 nm

grating has 600 lines /mm

d = 1/600 mm = 1.67 E-6 m

y1 = D/d = D 589.522E-9 / 1.67E-6 = 0.3530 D

y2 = D* 588.995E-9/ 1.67E-6 = 0.3527 D

we want y1 -y2 = 0.0003D = 10*1.7 = 17 nm

D = 17E-9 / 0.0003 = 5.667 E-5 m

The distance is too small for the camera to be positioned correctly.

c) the question is not connected.