Question
Answer all questions, show all work. Solution is there to check your work. "(Solution)"
Two narrow slits d = (200.0 0.6) mu m apart are illuminated with light and the interference fringes on the screen are shown below. The distance between the slit and the screen is (0.50 0.01) m. What is the wavelength ( lambda ) and the uncertainty in the wavelength ( lambda ) of light used in this experiment?. The scale shown in the picture below has an uncertainty of 0.5 mm (1000 100) nm (hints: use the position of the bright fringe, ym = m lambda L/d) The laser light is illuminated through a single slit of width a = (20.0 0.5) mu m and the diffraction pattern is shown in the picture below. The distance between the slit and the screen is (1.50 0.01) m. Calculate in proper form. (22 3) nm (hints: use the position of the dark fringe for the single slit as ym = m lambda L/a) The figure below shows interference pattern when a laser is shined through a double slit. The intensity on both sides decreases with distance away from the centerbecause of diffraction effect. The scale is attached at the bottom. The distance between the slit and the screen is L = 0.5 m. The wavelength of the light (laser) used is 700 nm(1nm = 10-9m.) Find the slit separation d. (Hint: Use double slit interference formula to locate the positions of the bright spots.) (~ 150 mu m) Find the slit width a.(Hint: Use single slit diffraction formula to locate the positions of darks spots.)(~22 mu m) 8. We shine light onto a diffraction grating with N = 550 lines/mm. (position of bright fringe (only this formula will be given in the formula sheet): d.sin theta = m lambda, where m = 0, 1, 2, 3... and 'd' is the separation between two lines = 1/N) . Work out the angles for all orders of diffraction maxima for blue light of wavelength 450 nm (14.3 degree, 29.6 degree , 47.9 degree, 81.5 degree)
Explanation / Answer
5. ) Assume (lamda=v) (delata=D)
V=Yd/mL=200*(10^-6)*5*10^-3/(2*.50)=1000nm
Error in V is written as: DV/V=DY/Y+Dd/d+DL/L=(0.5/5)+(.6/200)+(0.01/0.50)=0.1
DV/V=0.1; DV=V*0.1=1000nm*0.1=100nm
6.)
V=aY/mL=200*(10^-6)*5*10^-3/(3*1.50)=22.22nm
Error in V is written as: DV/V=DY/Y+Dd/d+DL/L=(0.5/5)+(.5/20)+(0.01/1.50)=0.13
DV/V=0.13; DV=V*0.13=22.22nm*0.13=2.92nm
7).
a) d=VmL/Y=700*(10^-9)*0.5*2/(4.5*10^-3)=155 micro meter
b) a=VmL/Y=700*(10^-9)*0.5*2/(2*4.5*10^-3)=75 micro meter
8)
dsin@=mv (lamda=v)(@= angle)
@=inverse sin(mv/d) but d=1/N
@=inverse sin(mvN)
@=inverse sin(1*450*10^-9*550/10^-3)=14.3 ; m=1
@=inverse sin(2*450*10^-9*550/10^-3)=29.6 ; m=2
@=inverse sin(1*450*10^-9*550/10^-3)=47.9 ; m=3
@=inverse sin(1*450*10^-9*550/10^-3)=81.5 ;m=4
