1. A Nd:YAG laser (wavelength of 532 nm) shines through a single slit >of unknow

Question

1. A Nd:YAG laser (wavelength of 532 nm) shines through a single slit
>of unknown width D onto a screen 2.00 m away from the slit. The
>distance on the screen between the m = 1 minima on either side of the
>central maximum of the diffraction pattern is measured and is found
>to be 2.3 cm. What is the width D of the slit?
>

>2. A Ti:Sapphire (Ti:Aluminum Oxide) laser (wavelength 800 nm) shines
>through a double slit of unknown separation d onto a screen 2.00 m
>away from the slit. The distance on the screen between the m = 4
>maxima on either side of the central maximum of the two-slit
>diffraction pattern is measured and is found to be 3.4 cm. What is
>the separation d of the two slits?

Explanation / Answer

Use the equation for single slit minima:

d*sin(theta) = n*lambda

where d is slit width, theta is angle between dark fringes (intensity minima), n is diffraction order, lambda is wavelength.

if the distance to the screen is D, the distance between the center line and minimum, y, is

y = L*tan(theta)

since theta is small, tan(theta) = theta(radians) = sin(theta)

D*sin(theta) = n*lambda

but sin(theta) = tan(theta) = y/D, so we have

D*y/L =n*lambda

D = L n lambda/ y

n=1

y=2.3/2=1.15

D = 2.00m * 1 x 532x10^-9 m/1.15m = 9.25*10^-7 m

Use the equation for double slit maxima:

d*sin(theta) = n*lambda

where d is slit width, theta is angle between dark fringes (intensity minima), n is diffraction order, lambda is wavelength.

D = L n lambda/ y

n=4

y=3.4/2=1.7

D = 2.00m * 4 * 800*10^-9 m/1.7m = 3.76*10^-6 m

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