A double slit system contains two slits that are separated by a distance of 200,

Question

A double slit system contains two slits that are separated by a distance of 200, 000 nm. Blue light of wavelength 400 nm shines on the double slit, and an interference pattern (series of equally spaced bright and dark spots) appears on a screen that is 2.4 meters away. The central bright spot of the pattern is labeled y = 0 on the screen. (1 nm = 10-9 ra) [Wow, those angles are probably pretty small ..].What is the angle (in degrees) to the 2nd bright spot away from the central bright? How far apart (in meters) on the screen are the third bright spot on one side and the 4th dark spot on the other side? If the individual slits in the double slit were made wider (but still having the same separation between the two slits) explain in words what change would you notice on the pattern of bright spots on the screen?

Explanation / Answer

Remembet this for future problems:
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n interfreence or diffraction pattern

the needed equation is Y = mLR/d---------------1

and d sin theta = mL--------------------2

where L = wavelgnth

m = order = 1,2,3,4, ......... for brigth bands

m = 1.5, 2.5, 3.5, 4.5, ......for dark bands

R is the distance from slit to screen

Y = disatnce from central spot to nth order fringe or fringe width
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so here we now apply

a. d sin theta = mL

sin theta = 2* 400nm/200000nm)

sin theta = 0.004

theta = 0.229 deg
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b. Y4-Y3 = (3.5-3) * 400nm * 2.4/(200000nm)

DY = 0.0024 m
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c. if no. of lines on slit in increased, higher no. fringes will be observed on screen and thier intentisty also increases

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