Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the oscillation/wave problem: Two coherent light sources of 600 nm wavelength. For constructive interference, what must be the path difference? For destructive? $\Delta x=n\lambda$ for bright; $\Delta x=(n+\tfrac{1}{2})\lambda$ for dark Step 1: Constructive: $\Delta x=n\lambda=0,600,1200,\ldots$ nm. Step 2: Destructive: $\Delta Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave…

Problem Statement Solve the oscillation/wave problem: In YDSE, fringe width is 0.5 mm with $\lambda=500$ nm. New fringe width if $\lambda=600$ nm (other parameters unchanged)? $\beta\propto\lambda$ Step 1: $\beta\propto\lambda$; $\beta’=0.5\times(600/500)=0.6$ mm. $$\boxed{\beta’=0.6\text{ mm}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical…

Problem Statement YDSE: fringe width 1 mm when $d=1$ mm. New width if $d$ doubled? Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or…

Problem Statement YDSE: $d=1$ mm, $D=1$ m, $\lambda=600$ nm, screen width 12 mm. How many bright fringes are visible? Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify…

Problem Statement YDSE as above ($d=2$ mm, $D=1.5$ m, $\lambda=500$ nm). Position of 3rd dark fringe from center? Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which…

Problem Statement Solve the elasticity problem: In Young’s double slit experiment: $d=1.0$ mm, $D=1.0$ m, $\lambda=589$ nm. Find fringe width. $\beta=\lambda D/d$ Step 1: $\beta=\lambda D/d=589\times10^{-9}\times1.0/10^{-3}=5.89\times10^{-4}$ m $=0.589$ mm. $$\boxed{\beta=0.589\text{ mm}}$$ Given Information Material’s Young’s modulus $Y$ or Bulk modulus $B$ or Shear modulus $G$ Dimensions (length $L$, area $A$) and applied force or pressure…

Problem Statement YDSE: $d=2$ mm, $D=1.5$ m, $\lambda=500$ nm. Find position of the 3rd bright fringe from center. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which…

Problem Statement Solve the optics problem: A light ray travels 4 cm in glass ($n=1.5$). Find the optical path length. Optical path $=nd$ Step 1: Optical path $=n\times d=1.5\times4=6$ cm. $$\boxed{\text{Optical path}=6\text{ cm}}$$ Given Information Refractive index $n$ or focal length $f$ as given Object distance $u$ (negative for real objects in Cartesian convention) Radius…

Problem Statement Solve the kinematics problem: Refractive index of water = 1.33. Find speed of light in water. $v=c/n$ Step 1: $v=c/n=3\times10^8/1.33\approx2.26\times10^8$ m/s. $$\boxed{v\approx2.26\times10^8\text{ m/s}}$$ Given Information Initial velocity $u$ (or $v_0$) Acceleration $a$ (constant unless stated otherwise) Time $t$ or distance $s$ as given Physical Concepts & Formulas Kinematics describes motion without reference to…

Problem Statement Solve the oscillation/wave problem: Wavelength of light in vacuum is 589 nm. Find its wavelength in glass of refractive index 1.5. $\lambda_{medium}=\lambda_{vacuum}/n$; frequency unchanged Step 1: $\lambda_{glass}=\lambda_{vacuum}/n=589/1.5\approx392.7$ nm. $$\boxed{\lambda_{glass}\approx393\text{ nm}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical Concepts…