A laser beam with light of wavelength of 550 nm passes through a double slit and

Question

A laser beam with light of wavelength of 550 nm passes through a double slit and falls on a screen exactly 101 cm away.

(a) If the second bright band on the screen is found to be 1.821 cm away from the central bright band, what must be the slit separation in the double slit?

(b) You now use a different laser beam and a different double slit. If the wavelength of the new laser beam is 742 nm, and the first dark band appears on the screen 0.4029 cm away from the central bright band, what must be the slit separation in the new double slit?

Explanation / Answer

(a) ans

given that

wavelength =550nm

screen distance D=1.01 m

order of fringe n=2

position y=1.821*10^-2 m

now we find the slits seperation

d(y/D)=n*wavelegth

d(1.821*10^-2/1.01)=2*550*10^-9

slis seperation d=61*10^-6 m

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(b) ans

Given that

wavelength=742*10^-9 m

screen distance D=1.01 m

position of dark band y=0.4029 cm

order of dark fringe n=1

now we find the slit seperation

d(y/D)=(2n-1)*wavelength/2

d(4.029*10^-3/1.01)=(2*1-1)*742*10^-9/2

d=93*10^-6 m

therefore the new slit seperation =93*10^-6 m

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