Category: HC Verma Part 1: Waves & Optics

Problem Statement In problem 29, how many bright fringes of $\lambda=500$ nm appear between center and point P? 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 YDSE: $D=1.5$ m, $\lambda=589$ nm, fringe width 0.98 mm. Find slit separation. 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 field…

Problem Statement YDSE: $d=2$ mm, $D=2$ m. A point P is 3 mm from center. Find path difference at P. 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…

Problem Statement A soap film of thickness 300 nm ($n=1.33$) is illuminated by white light. Which wavelengths are strongly reflected? 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…

Problem Statement YDSE: $d=1$ mm, $D=1$ m, $\lambda=600$ nm, $\beta=0.6$ mm. Screen moved to $D=2$ m. New fringe width? 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 Solve the oscillation/wave problem: Why must two sources in an interference experiment be coherent? What is coherence? Incoherent sources: time-averaged $\langle\cos\delta\rangle=0$; no fringes Step 1: Coherent sources maintain a constant phase difference. Incoherent sources have random phase differences that change rapidly, causing i Given Information Mass $m$ and spring constant $k$ (or equivalent),…

Problem Statement Find the minimum thickness of an anti-reflection coating ($n=1.38$) on glass ($n=1.5$) for 550 nm light. 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 oscillation/wave problem: Two point sources of wavelength 500 nm are 1.5 mm apart. At what distances along the perpendicular bisector does constructive interference occur at screen 1 m away? $y_n=n\lambda D/d$ Step 1: Constructive at $y_n=n\lambda D/d=n\times500\times10^{-9}\times1/(1.5\times10^{-3})=n\times3.33\times10^{-4} Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial…

Problem Statement Two coherent sources of equal amplitude $a$ interfere. Express resultant intensity as function of phase difference $\delta$. 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 Solve the oscillation/wave problem: Two coherent sources of amplitudes $a_1=3$ and $a_2=1$ interfere. Find $I_{max}/I_{min}$. $I_{max}/I_{min}=\left(\frac{a_1+a_2}{a_1-a_2}\right)^2$ Step 1: $I_{max}=(a_1+a_2)^2=16$; $I_{min}=(a_1-a_2)^2=4$. Step 2: $I_{max}/I_{min}=16/4=4$. $$\boxed{I_{max}/I_{min}=4}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical Concepts & Formulas Simple harmonic motion arises…