In the Young's double slit experiment, the distance between the slits varies in time as $\mathrm{d}(\mathrm{t})=\mathrm{d}_{0}+\mathrm{a}_{0} \sin \omega \mathrm{t} ;$ where $\mathrm{d}_{0}, \omega$ and $\mathrm{a}_{0}$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :
$\frac{2 \lambda D\left(d_{0}\right)}{\left(d_{0}^{2}-a_{0}^{2}\right)}$
$\frac{2 \lambda \mathrm{Da}_{0}}{\left(\mathrm{~d}_{0}^{2}-\mathrm{a}_{0}^{2}\right)}$
$\frac{\lambda \mathrm{D}}{\mathrm{d}_{0}^{2}} \mathrm{a}_{0}$
$\frac{\lambda \mathrm{D}}{\mathrm{d}_{0}+\mathrm{a}_{0}}$
Correct Option: , 2
Fringe Width, $\beta=\frac{\lambda D}{d}$
$\beta_{\max } \Rightarrow d_{\min }$ and $\beta_{\min } \Rightarrow d_{\max }$
$\mathrm{d}=\mathrm{d}_{0}+\mathrm{a}_{0} \sin \omega \mathrm{t}$
$\mathrm{d}_{\max }=\mathrm{d}_{0}+\mathrm{a}_{0}$ and $\mathrm{d}_{\min }=\mathrm{d}_{0}-\mathrm{a}_{0}$
$\therefore \beta_{\min }=\frac{\lambda \mathrm{D}}{\mathrm{d}_{0}+\mathrm{a}_{0}}$ and $\therefore \beta_{\max }=\frac{\lambda \mathrm{D}}{\mathrm{d}_{0}-\mathrm{a}_{0}}$
$\beta_{\max }-\beta_{\min }=\frac{\lambda \mathrm{D}}{\mathrm{d}_{0}-\mathrm{a}_{0}}-\frac{\lambda \mathrm{D}}{\mathrm{d}_{0}+\mathrm{a}_{0}}=\frac{2 \lambda \mathrm{Da}_{0}}{\mathrm{~d}_{0}^{2}-\mathrm{a}_{0}^{2}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,