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Double and Single slit equations revised.. 
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#1
Nov2707, 05:00 PM

P: 263

Hi, I had already posted a thread on this topic, but since it was getting really messy, I decided to start a fresh thread. Please reply to this thread.
Please check my solutions: Calculate the angle that will form between the centre maximum and the thirdorder dark fringe if the wavelength of the light that strikes two slits is 650 nm and the distance between the slits is 2.2 106 m. 1. n=3, λ=6.5* m, d=2.2* m (n0.5)λ= d*Sinθ Sinθ= (n0.5)*λ/d = (30.5)6.5* /2.2* = 2.5*6.5* /2.2 = 7.3863*0.1= 0.73863 Sinθ= 0.73863 θ= (0.73863)= 47.61 degrees 2)In an experiment, blue light with a wavelength of 645 nm is shone through a doubleslit and lands on a screen that is located 1.35 m from the slits. If the distance from the centre maximum to the 8th order bright fringe is 2.6 cm, calculate the distance between the two slits. 2. m=8, λ=6.45* m, L =1.35m, X=0.026m X/L=mλ/d d=Lmλ/X d= 1.35*6.45* *8/0.026 =2.68* m 3)In an experiment, the distance from one slit to the third dark fringe is found to be 2.200 046 8 m. If the wavelength of the light being shone through the two slits is 590 nm, calculate the distance from the second slit to this same dark fringe. 3. n=3, PS1= 2.2000468m,λ=5.9* m (n0.5)λ=lPS1PS2l +/ (30.5)5.9* = 2.2000468PS2 +/ 14.75* = 2.2000468PS2 PS2= 2.200046814.75* OR 2.2000468+14.75* PS2= 2.200045325m or 2.200048275m 4)Two slits are separated by a distance of 2.00 105 m. They are illuminated by light of wavelength 5.60 107 m. If the distance from the slits to the screen is 6.00 m, what is the separation between the central bright fringe and the third dark fringe? 4. X/L= (2n+1)λ/2d X= (2n+1)λL/2d= 42*5.60*106/4*105 = 58.8*102= 0.60m Light of wavelength 625 nm shines through a single slit of width 0.32 mm and forms a diffraction pattern on a flat screen located 8.0 m away. Determine the distance between the middle of the central bright fringe and the first dark fringe λ=6.25*〖10〗^(7)m, w=0.32*〖10〗^(3)m, L=8.0m λ/w=X/L X=Lλ/w= 8*6.25*〖10〗^(7)/0.32*〖10〗^(3) 1.56*〖10〗^2m Light of 600.0 nm is incident on a single slit of width 6.5 mm. The resulting diffraction pattern is observed on a nearby screen and has a central maximum of width 3.5 m. What is the distance between the screen and the slit? λ=6.00*〖10〗^(7)m, w=6.5*〖10〗^(3)m, 2X=3.5;X=1.75m λ=wX/L L=wX/λ= 6.5*1.75*〖10〗^(3)/6*〖10〗^(7)= 11.375*〖10〗^4/6 =2.00*〖10〗^4m A monochromatic beam of microwaves with a wavelength of 0.052 m is directed at a rectangular opening of width 0.35 m. The resulting diffraction pattern is measured along a wall 8.0 m from the opening. What is the distance between the first and secondorder dark fringes? λ=0.052m, w=0.35m, L=8m λ/w=X/L X= Lλ/w= 8*0.052/0.35 = 1.18 m Light from a red laser passes through a single slit to form a diffraction pattern. If the width of the slit is increased by a factor of two, what happens to the width of the central maximum? λ1=wy1/L, y1= Lλ/w λ2=2wy/L, y2= Lλ/2w y2/y1= λ2L*w/2w*Lλ1 y2/y1= 0.5 y2=0.5y1 Light of wavelength 600 nm is incident upon a single slit with width 4.0 × 104 m. The figure shows the pattern observed on a screen positioned 2.0 m from the slits. (image attached) I am unclear on this one:weather to use X=lnwavelength/w or (m+0.5)wavelength=wX/L 


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