Difrraction Question - AS level Watch

php_cat_tsr
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#1
Report Thread starter 8 years ago
#1
Hi,

Another question which I cant seem to get right!
'The interference patterns from a diffraction grating and a double slit are compared.
Using the diffraction grating, yellow light of the first order is seen at 30° to the normal to the
grating.
The same light produces interference fringes on a screen 1.0 m from the double slit. The slit
separation is 500 times greater than the line spacing of the grating.
What is the fringe separation on the screen?
A
2.5 × 10–7 m

B
1.0 × 10–5 m

C
1.0 × 10–3 m

D 1.0 × 10–1 m
0
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Stonebridge
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#2
Report 8 years ago
#2
For the diffraction grating
nλ = dsinθ
n=1 (1st order)
θ = 30 deg so sinθ= 0.5
Equation is
λ = 0.5d where d is the grating spacing

For the double slits the equation is
λ = ay/x where a is the slit separation, x is the distance to the screen, y is fringe spacing.
x=1 meter so the equation is
λ = ay

As it is the same wavelength in each case we can equate the two equations to give
0.5d = ay where y is the fringe spacing we want to find.
We also know that a is 500 times d
So put a=500d in the equation, cancel out d, and get a value for y.
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