This chapter covers the principles and phenomena of wave optics, including interference, diffraction, and polarization, highlighting their significance in understanding light behavior.
WAVE OPTICS – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the WAVE OPTICS chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
v = fλ
v is the wave speed (m/s), f is the frequency (Hz), and λ is the wavelength (m). This formula relates the speed of a wave to its frequency and wavelength.
n = c/v
n is the refractive index (dimensionless), c is the speed of light in vacuum (≈ 3 × 10^8 m/s), and v is the speed of light in the medium (m/s). It describes how light slows down in different media.
n₁ sin(θ₁) = n₂ sin(θ₂)
This is Snell's law, where n₁, n₂ are the refractive indices of the two media and θ₁, θ₂ are the angles of incidence and refraction, respectively. It describes how light bends when entering a different medium.
sin i = (v₁/v₂) sin r
Where i is the angle of incidence, r is the angle of refraction, v₁ and v₂ are speeds of light in the first and second medium, respectively. It helps find the angle when light passes between media.
λ₂ = (v₂/v₁)λ₁
This relates the wavelengths λ₁ and λ₂ in two media with speeds v₁ and v₂. It shows how wavelength changes when light moves from one medium to another.
d sin θ = nλ
d is the distance between slits, θ is the angle of the fringe from the central maximum, n is the order of the fringe, and λ is the wavelength. This is used in Young's double-slit experiment to describe interference.
I = I₀ + 2√(I₀I_1) cos(ΔΦ)
I is the resultant intensity, I₀ and I₁ are the intensities of two coherent sources, and ΔΦ is the phase difference. This relation is crucial in analyzing interference patterns.
θ_min = (nλ)/a
θ_min represents the angles of minima in single-slit diffraction, n is the order of the minimum, λ is the wavelength, and a is the width of the slit. This describes how diffraction patterns form.
I = I₀ cos²(θ)
Where I is the intensity transmitted through two polaroids, I₀ is the initial intensity, and θ is the angle between the pass axes of the polaroids. This is known as Malus' Law in polarization.
λ = (c/f)
Where λ is the wavelength, c is the speed of light in vacuum, and f is frequency. This equation is fundamental in wave optics related to light waves.
Equations
n = sin(θ₁)/sin(θ₂)
This is the refractive index formula derived from Snell's law, illustrating the ratios of sines of the angles of incidence and refraction.
I = 4I₀ for constructive interference
The maximum intensity occurs when two waves are completely in phase, demonstrating the principle of constructive interference.
I = 0 for destructive interference
The intensity is zero when the path difference is (n + 1/2)λ, indicating perfect cancellation.
v = c/n
This describes the speed of light in a medium (v) in relation to the speed of light in vacuum (c) and the refractive index (n) of the medium.
Δy = (λL)/d
Δy is the fringe separation on a screen at distance L from the slits, λ is the wavelength of light, and d is the distance between the slits in Young's experiment.
r = (n + 1/2)λ
This describes the path difference leading to a dark fringe in fringe patterns, where n is an integer.
r = nλ
This describes the path difference leading to a bright fringe, where n is an integer.
n_1 * λ_1 = n_2 * λ_2
Describes the relation between the wavelengths of light in different media concerning their refractive indices.
λ = (xD)/(d)
This derives the wavelength from the fringe distance (x), distance to the screen (D), and distance between the slits (d) in Young's experiment.
cos²(θ) = (1 + cos(2θ))/2
This relates the cosine term in intensity calculations to trigonometric identities useful in wave interference.
This chapter explores the behavior of light through ray optics, focusing on reflection and refraction. It is essential for understanding optical instruments and the functioning of the human eye.
Start chapterThis chapter explores the dual nature of radiation and matter, focusing on how light behaves both as a wave and a particle. Understanding this duality is key to grasping modern physics concepts.
Start chapterThis chapter explores the atomic structure, detailing the models of atoms proposed by J.J. Thomson and Ernest Rutherford. Understanding these concepts is crucial for grasping the foundation of modern physics.
Start chapterThis chapter explains the structure and properties of atomic nuclei, including their components, stability, and phenomena like radioactivity, fission, and fusion.
Start chapterThis chapter explores the fundamentals of semiconductor electronics, including materials, devices, and basic circuits. Understanding these concepts is crucial for grasping modern electronic technology.
Start chapter
