Contents
Wave Optics
Complete Chapter Notes & 70 Q&A Bank
Class 12 CBSE • JEE/NEET Foundation
📝 Syllabus
- Wavefront & Huygen’s principle.
- Refraction & Reflection via Huygen’s principle.
- Coherent sources & Interference.
- Young's double slit experiment (YDSE) & Fringe width.
- Diffraction due to a single slit.
1. Huygen’s Principle
Wavefront: Locus of all particles vibrating in the same phase.
- Point Source: Spherical Wavefront.
- Distant Source: Plane Wavefront.
- Linear Source: Cylindrical Wavefront.
💡 Memorize: Rays are always perpendicular to the wavefront.
2. YDSE (Interference) Formulas
If $d$ = slit distance, $D$ = screen distance, $\lambda$ = wavelength.
Path Diff: $\Delta x = \frac{yd}{D}$
Fringe Width: $\beta = \frac{\lambda D}{d}$
Conditions:
- Bright (Max): $\Delta x = n\lambda$
- Dark (Min): $\Delta x = (2n-1)\frac{\lambda}{2}$
💡 Trick: "Bright" needs integers ($n$). "Dark" needs halves ($0.5, 1.5$).
3. Diffraction (Single Slit)
Bending of light around corners ($a \approx \lambda$).
Minima (Dark): $a \sin \theta = n\lambda$
Central Max Width: $\beta_0 = \frac{2\lambda D}{a}$
Note: Central max is double the width of secondary maxima.
🔥 70 Important Questions
Tap questions to see answers
VSA 1. What is the shape of wavefront from a point source?
Spherical wavefront.
VSA 2. Define coherent sources.
Sources that emit light of the same frequency and have a constant initial phase difference.
VSA 3. What is the phase difference on a wavefront?
Zero. All points on a wavefront oscillate in the same phase.
VSA 4. Relation between phase diff ($\phi$) and path diff ($\Delta x$).
$\phi = \frac{2\pi}{\lambda} \Delta x$
VSA 5. Can two independent bulbs produce interference?
No, because they are incoherent (phase difference changes randomly).
VSA 6. How does fringe width change in water?
It decreases. $\beta' = \beta / \mu$.
VSA 7. Shape of wavefront for light from infinity?
Plane wavefront.
VSA 8. What is conserved in interference?
Energy is conserved (redistributed).
VSA 9. Locus of points with constant path difference in YDSE?
Hyperbola.
VSA 10. Why is sound diffraction easier to observe than light?
Sound wavelength is large (comparable to daily obstacles), light wavelength is very small.
VSA 11. Condition for diffraction?
Size of obstacle ($a$) $\approx$ Wavelength ($\lambda$).
VSA 12. Effect of increasing $D$ on fringe width?
$\beta \propto D$, so fringe width increases.
VSA 13. Intensity at path difference $\lambda/2$?
Zero (Destructive interference).
VSA 14. Effect of slit width ($a$) on diffraction width?
Angular width $\propto 1/a$. If slit width increases, central max becomes narrower.
VSA 15. Angle between ray and wavefront?
90 degrees.
SA 16. State Huygen’s Principle.
Every point on a wavefront acts as a source of secondary wavelets. The forward envelope of these wavelets gives the new wavefront.
SA 17. Wavefront emerging from a convex lens (source at focus)?
Plane wavefront (rays become parallel).
SA 18. Why no interference from two candles?
They are incoherent sources. Phase difference varies rapidly, averaging intensity to uniform brightness.
SA 19. Ratio $A_1:A_2 = 3:1$. Find $I_{max}:I_{min}$.
$\frac{I_{max}}{I_{min}} = (\frac{3+1}{3-1})^2 = (\frac{4}{2})^2 = 4:1$.
SA 20. Diff between Interference and Diffraction?
Interference: Superposition of two coherent sources. Diffraction: Superposition of wavelets from same wavefront.
SA 21. Width of central max vs secondary max in diffraction?
Central max width ($2\lambda D/a$) is twice the width of secondary maxima ($\lambda D/a$).
SA 22. Yellow light replaced by Blue in diffraction?
$\lambda_{blue} < \lambda_{yellow}$. Since width $\propto \lambda$, the pattern becomes narrower.
SA 23. Why is sustaining interference hard?
It requires perfectly coherent sources and stable environment to maintain constant phase difference.
SA 24. Plane wavefront through a prism?
Emerges as a plane wavefront but tilted towards the base of the prism.
SA 25. Why is the sky blue?
Scattering $\propto 1/\lambda^4$. Blue (short $\lambda$) scatters more than red.
SA 26. In YDSE, if $d$ increases?
$\beta \propto 1/d$. Fringe width decreases (fringes get closer).
SA 27. Effect of wide source slit?
Acts as multiple incoherent sources, causing overlapping patterns and loss of contrast (fringe washout).
SA 28. Define Linear Width of Central Max.
Distance between first minima on either side of center. $\beta_0 = 2D\lambda/a$.
SA 29. Can sound be polarized?
No, because sound is a longitudinal wave. Only transverse waves (light) can be polarized.
SA 30. Why TV picture shakes when plane passes?
Interference between direct signal and signal reflected from the plane causes fluctuating intensity.
NUM 31. YDSE: $\lambda_1=12000, \lambda_2=10000$. Coincidence?
Condition $n_1 \lambda_1 = n_2 \lambda_2$. Ratio $5:6$. 5th fringe of $\lambda_1$ coincides with 6th of $\lambda_2$.
NUM 32. Frequency $6\times10^{14}$Hz, $d=1$mm, $D=1$m. Find $\beta$.
$\lambda = c/\nu = 500$nm. $\beta = \frac{1 \times 500 \times 10^{-9}}{10^{-3}} = 0.5$mm.
NUM 33. Ratio of intensities for path diff $\lambda/4$ and $\lambda/3$.
$\phi_1 = \pi/2 \to I = I_0/2$. $\phi_2 = 2\pi/3 \to I = I_0/4$. Ratio $2:1$.
NUM 34. 1st Min of Red (660nm) = 1st Max of $\lambda'$. Find $\lambda'$.
$1 \cdot \lambda_R = 1.5 \cdot \lambda'$. $\lambda' = 660/1.5 = 440$nm.
NUM 35. Angular width for $\lambda=6000\mathring{A}, a=1$mm.
$2\theta = 2\lambda/a = 1.2 \times 10^{-3}$ radians.
NUM 36. Intensity of 1st secondary max vs central max?
Approx 4.5% of central intensity ($I_0/22$).
NUM 37. YDSE with White Light?
Central fringe white. Others colored (violet near center, red far).
NUM 38. Phase diff for constructive interference?
$2n\pi$ (Even multiple of $\pi$).
NUM 39. One slit covered in YDSE. Intensity change?
If $I_{max} = 4I_0$, covering one slit makes intensity $I_0$. It becomes $1/4$th of max.
NUM 40. Slit width $a$ for $30^\circ$ diffraction with 650nm.
$a \sin 30 = \lambda \Rightarrow a(0.5) = 650 \text{nm} \Rightarrow a = 1.3 \mu \text{m}$.
SA 41. Why soap bubbles colored?
Interference of light reflected from top and bottom surfaces of thin film.
SA 42. Resolving power of telescope vs aperture?
R.P $\propto$ Diameter. Larger aperture = better resolution.
SA 43. Path diff for 1st secondary max?
$3\lambda/2$.
SA 44. Does diffraction width depend on distance?
Yes, linear width $\propto D$.
SA 45. Glass sheet in front of one slit (YDSE)?
Pattern shifts towards the glass sheet side. Fringe width remains same.
SA 46. Define sustained interference.
Positions of Maxima and Minima do not change with time.
SA 47. Why central diffraction max bright?
Constructive interference of wavelets from the entire slit width.
SA 48. Intensity at dark fringe (identical slits)?
Zero.
SA 49. Define Fresnel distance.
$Z_F = a^2/\lambda$. Distance where diffraction spread equals slit size.
SA 50. Shape of YDSE fringes?
Hyperbolic.
VSA 51. Energy lost at dark fringe?
No, it shifts to bright fringe.
VSA 52. Resolving power vs Wavelength?
Inversely proportional. Higher $\lambda$ = Lower resolution.
VSA 53. Huygen's principle for sound?
Yes, valid for all waves.
VSA 54. Phase diff between E and B in EM wave?
Zero.
VSA 55. Can X-rays diffract?
Yes, by crystals (Bragg's Law).
VSA 56. Slit width ratio 4:9. Amplitude ratio?
$W \propto A^2 \Rightarrow A \propto \sqrt{W}$. Ratio is $2:3$.
VSA 57. Does refractive index depend on $\lambda$?
Yes (Cauchy's formula).
VSA 58. Speed of light in reflection?
Unchanged.
VSA 59. What is D in $\beta = D\lambda/d$?
Distance between slit plane and screen.
VSA 60. Condition for destructive interference?
Path difference = Odd integral multiple of $\lambda/2$.
SA 61. Source moved closer to slits (YDSE)?
No change in fringe width ($\beta$).
SA 62. Wavefront of linear source?
Cylindrical.
SA 63. Snell’s law in velocities?
$\sin i / \sin r = v_1 / v_2$.
SA 64. Why central fringe bright?
Path difference is zero $\to$ Constructive interference.
SA 65. Interference with wide slit?
Not visible.
SA 66. Fringes in central diffraction peak?
Count $\approx 2d/a$.
SA 67. Red filter on slit 1, Blue on slit 2?
No interference (incoherent, different $\nu$).
SA 68. Intensity ratio 1:4. Min Intensity?
$(\sqrt{4}-\sqrt{1})^2 = 1$ unit.
SA 69. Why light diffraction rare in daily life?
Wavelength is too small compared to obstacles.
SA 70. Is speed of light relative?
No, it is constant for all observers.
⚠️ Important: Practice These Diagrams
To get full marks in 3-mark and 5-mark questions, you must practice drawing these diagrams with a pencil/ruler:
- ✏️ Huygen's Principle: Refraction and Reflection of a plane wavefront (showing triangles for proof).
- ✏️ YDSE Setup: Showing path difference $S_2P - S_1P$.
- ✏️ Intensity Graphs:
(a) Interference (All peaks same height).
(b) Diffraction (Central peak double width, intensity decreases).
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