SME
Grade 11 Science · Problem type
Double-slit interference
Use this for “Laser light (633 nm) passes two slits 0.25 mm apart onto a screen 2 m away. How far apart are the bright fringes?”
Diagram
Δy = λL/d
Δy
=
633 ×
10
-9
m
×
2
m/(0.25
×
10
-3
m)
Δy = 5.06 mm
Bright where the paths from the two slits differ by a whole number of wavelengths (mλ), dark halfway between.
This is an example. Type your own values to start a new problem.
Δy (mm)
=
λ (nm)
×
L (m)
d (mm)
Formulas
Δy
=
λ
×
10
-9
×
L
/(
d
×
10
-3
)
×
1,000
5.06
=
633 ×
10
-9
×
2/(0.25
×
10
-3
)
×
1,000
Assumptions
•
Each slit spreads the light out (diffraction); where the two overlap they interfere.
•
Bright where the waves arrive in step, dark where they cancel.
•
Bright fringes are Δy = λL/d apart, with the screen far away compared with d.
Step-by-step
WE KNOW
λ = 633 nm, d = 0.25 mm, L = 2 m
FIND
fringe spacing (Δy)
Step 1 · Find fringe spacing (Δy)
Use Δy = λ × 10⁻⁹ × L/(d × 10⁻³) × 1,000
λL/
d
in
meters
(1
nm
=
10
-9
m,
1
mm
=
10
-3
m),
then
×
1,000
for
mm.
Δy
=
633 ×
10
-9
×
2/(0.25
×
10
-3
)
×
1,000
λ
=
633
nm
=
6.33 ×
10
-7
m
d
=
0.25
mm
=
2.5 ×
10
-4
m
Δy
=
6.33 ×
10
-7
×
2/(2.5
×
10
-4
)
=
0.005064
m
Δy = 5.06 mm
Check
Put the numbers back in. Both sides should match.
5.06
≈
633 ×
10
-9
×
2/(0.25
×
10
-3
)
×
1,000
✓
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