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Just a basic waves formula sheet with diagrams. Made it in senior physics but found it useful in first year physics also. Good for when your first getting familiar with single-double slit difraction, dark-bright bands etc
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DIFRACTION GRATINGS-use double slit formula
DIFRACTION-Double slit
antinodal – bright band
𝑺𝟏𝑷− 𝑺𝟐𝑷 = 𝒏𝝀
𝑛𝜆 = 𝑑 sin𝜃 𝑜𝑟 sin𝜃 =𝑛𝜆
𝑑
𝑖𝑓 𝜃 𝑖𝑠 𝑠𝑚𝑎𝑙𝑙 𝑡ℎ𝑒𝑛— sin𝜃 = tan𝜃
𝐻𝑒𝑛𝑐𝑒 𝑥 = 𝐿 sin𝜃 𝑜𝑟 sin𝜃 =𝑥
𝐿
∴ 𝒏𝝀
𝒅=𝒙
𝑳
nodal – dark band
𝑺𝟏𝑷 − 𝑺𝟐𝑷 = (𝒏 − 𝟏 𝟐 )𝝀
∴ (𝑛 − 1
2 )𝝀
𝒅=𝒙
𝑳
𝑺𝟏𝑷 = number of wave lengths from original1
𝑺𝟐𝑷 = number of wave lengths from original2
n = the number of waves from the original
𝛉 = the angle for the 1st bright band
x = distance to 1st bright band
L = distance to screen where is being projected
d = distance between slits
WIDTH OF CENTRAL MAXIMUM
𝑊𝑖𝑑𝑡ℎ 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑚𝑎𝑥 =𝑳𝝀
𝒅
𝑳 ↑ 𝑿 ↑ 𝑿 ↓ 𝑳 ↓ 𝒅 ↑ 𝑿 ↓ 𝑿 ↑ 𝒅 ↓
𝑶𝒓𝒅𝒆𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒍𝒂𝒔𝒕 𝒃𝒓𝒊𝒈𝒉𝒕 𝒇𝒓𝒊𝒏𝒈𝒆 𝒊𝒔 𝒘𝒉𝒆𝒓𝒆 𝜽 = 𝟗𝟎°
𝑨𝑵𝑮𝑼𝑳𝑨𝑹 𝑫𝑬𝑽𝑰𝑨𝑻𝑰𝑶𝑵 = 𝐬𝐢𝐧 𝜽 − 𝐬𝐢𝐧 𝜽
DIFRACTION-Single slit
Nodal -- Dark Band
𝑛𝜆 = 𝑤 sin𝜃 𝑜𝑟 sin𝜃 =𝑛𝜆
𝑤
𝑖𝑓 𝜃 𝑖𝑠 𝑠𝑚𝑎𝑙𝑙 𝑡ℎ𝑒𝑛— sin𝜃 = tan𝜃
𝐻𝑒𝑛𝑐𝑒 𝑦 = 𝐿 tan𝜃 𝑜𝑟 sin𝜃 =𝑦
𝐿
This is the formula for 1st dark band
∴ n=1
∴ 𝒏𝝀
𝒘=𝒚
𝑳 𝒐𝒓 𝒏𝝀 =
𝒘𝒚
𝑳
𝒚 = 𝑳𝝀
𝒘
Antinodal -- Bright Band
∴ (𝒏+ 𝟏 𝟐 )𝝀
𝒘=𝒚
𝑳 𝒐𝒓 (𝒏− 𝟏 𝟐 )𝝀 =
𝒘𝒚
𝑳
𝒚 = 𝑳(𝒏 + 𝟏 𝟐 )𝝀
𝒘
𝛉 = the angle for the 1st dark band
y = distance to 1st bright band
L = distance to screen where is being projected
w = distance between slits
WIDTH OF CENTRAL MAXIMUM
𝑊𝑖𝑑𝑡ℎ 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑚𝑎𝑥 =𝟐𝑳𝝀
𝒘
WIDTH OF 1ST ORDER BRIGHT FRINGE
(HALF WIDTH OF CENTRAL MAXIMUM)
𝑊𝑖𝑑𝑡ℎ =𝑳𝝀
𝒘
--------------------------------------------
For a biconvex lens
𝒇 =𝒓
𝟐(𝒏 − 𝟏)
PERIOD T of motion of light spring (where mass
of spring is negligible)
𝑻 = 𝟐𝝅 𝒎
𝒌
Displacement (x) SI UNIT=metres
Distance from equilibrium
Equilibrium (c)
Amplitude (a) SI UNIT=metres
Max displacement from equilibrium
sometimes reffered to as wave height
Large (a) suggests large amount of energy
Period (T) SI UNIT=seconds
Time it takes to complete 1 oscillation
Time to complete 1 cycle of vibration
𝑻 = 𝟏
𝒇
Frequency (f) SI UNIT=Hz
No. of oscillations per second
No. of cycles of vibration per second
𝒇 = 𝟏
𝑻 𝒇 =
𝒗
𝝀
Wavelength (ג) SI UNIT=metres
Minimum distance between 2 points in phase
ג =𝒗
𝒇
V = speed of the wave (constant) SI m/s
𝒗 =𝒅
𝒕 𝑽 = 𝒇 𝒗ג =
𝟏𝝀
𝑻
IF FREQUENCY REMAINS UNCHANGED
(as it generally does)
ג2
ג1
=𝑣2
𝑣1
Reflection of pulses
Boundary Reflected Pulse Transmitted
Pulse
Fixed end Out of phase ---
Free end In phase ---
Light to heavy
medium
Out of phase In phase
Heavy to light medium
In phase Out of phase
Mark Riley [email protected]
