Coherent light of frequency 6.38×10 14 Hz passes through two thin slits and fall

Question

Coherent light of frequency 6.38×1014 Hz passes through two thin slits and falls on a screen 80.0 cmaway. You observe that the third bright fringe occurs at ±3.15 cm on either side of the central bright fringe.

Part A

How far apart are the two slits?

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Part B

At what distance from the central bright fringe will the third dark fringe occur?

Coherent light of frequency 6.38×1014 Hz passes through two thin slits and falls on a screen 80.0 cmaway. You observe that the third bright fringe occurs at ±3.15 cm on either side of the central bright fringe.

Part A

How far apart are the two slits?

d =   mm  

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Part B

At what distance from the central bright fringe will the third dark fringe occur?

y =   cm  

Explanation / Answer

=c/f

= (3x108 m/s)/(6.38 x 1014 Hz)

= 4.7 x 10-7 m

We have sin = (3.15)/(802 +3.152)1/2 = 0.039

and m = d sin

So, d = m /sin

= 3 x 4.7 x 10-7/0.039 = 3.62 x 10-5 m

The third dark fringe corresponds to (m+1/2) = 5/2

sin = 5/2 (/d)

         = 5/2 x (4.7 x 10-7)/3.62 x 10-5 = 3.25 x10-2

The distance from the centre is Rtan

and tan = sin/(1- sin2)1/2

tan = 3.25 x10-2/[1-(3.25 x10-2)2]1/2 = 3.25 x 10-2

and distance x = R tan

                        = 80 x 3.25 x 10-2 = 2.60 cm

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