# Double and Single slit equations revised

1. Nov 27, 2007

### pinkyjoshi65

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 third-order dark fringe if the wavelength of the light that strikes two slits is 650 nm and the distance between the slits is 2.2 10-6 m.
1. n=3, λ=6.5* m, d=2.2* m
(n-0.5)λ= d*Sinθ
Sinθ= (n-0.5)*λ/d
= (3-0.5)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 double-slit 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
(n-0.5)λ=lPS1-PS2l
+/- (3-0.5)5.9* = 2.2000468-PS2
+/- 14.75* = 2.2000468-PS2
PS2= 2.2000468-14.75* OR 2.2000468+14.75*
PS2= 2.200045325m or 2.200048275m

4)Two slits are separated by a distance of 2.00 10-5 m. They are illuminated by light of wavelength 5.60 10-7 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*10-6/4*10-5
= 58.8*10-2= 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 second-order 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 × 10-4 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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