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 markriley85@hotmail.com