Two narrow slits 54 mu m apart are illuminated with light of wavelength 500 nm Y

Question

Two narrow slits 54 mu m apart are illuminated with light of wavelength 500 nm You may want to review What is the angle of the m = 2 bright fringe in radians? Express your answer using two significant figures. Theta_2 = rad What is the angle of the m = 2 bright fringe in degrees? Express your answer using two significant figures. theta_2 = Your friend has been given a laser for her birthday. Unfortunately, she did not receive a manual with it and so she doesn't know the wavelength that it emits. You help her b performing a double-slit experiment, with slits separated by 0.18 mm. You find that two adjacent bright fringes are 4.1 mm apart on a screen 1.4 m from the slits. What is the wavelength the laser emits? Express your answer to two significant figures and include the appropriate units. lambda =

Explanation / Answer

Given

   d= 54*10^-6 m

wavelength lambda = 500 nm = 500*10^-9 m

for constructive interference the condition is d sin theta = m*lamda

   sin theta2 = m*lambda /d

       = 2*500*10^-9 /(54*10^-6)

   theta2 = arc sin (0.0185185185185)

   Theta2 = 1.0611 degrees

PArt B

   we know that one radian = 57.2958 degrees

           so 1.0611 degrees = 0.01852 rad
so theta2 = 0.01852 rad

Part C

distance between two adjacent bright fringes is beta = 4.1 mm = 4.1*10^-3 m

   separation of slit to screen is D = 1.4 m
  
   slit separation d = 0.188*10^-3 m

  
we know that the fringe width is beta = m*Lmabda*D/d

   wavelength of the laser is

               Lambda = beta*d/(m*D)

               Lambda = (4.1*10^-3*0.188*10^-3)/(1*1.4) m

               Lambda = 5.50571*10^-7 m

               Lambda = 550 .571 nm

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