Coherence — Coherent sources
Wave Optics
8
JEE Qs
8%
Hard
40
min
Thoroughly understand the conditions for coherence and how practical setups like YDSE and thin films achieve them, as questions often test these underlying principles.
🧮 Key Formulas
✅ Key Points for JEE
- 1Coherent sources are sources that emit waves with a constant phase difference and the same frequency (and hence, wavelength).
- 2For sustained (stable and observable) interference patterns, the sources must be coherent. Without coherence, the phase difference randomly fluctuates, leading to an average intensity of I_1 + I_2 (no interference pattern).
- 3Two independent sources, even if monochromatic (same frequency), are never perfectly coherent over time due to random and rapid phase changes during emission.
- 4Coherent sources are typically achieved by deriving them from a single parent source using techniques like division of wavefront (e.g., Young's Double Slit Experiment) or division of amplitude (e.g., thin film interference, Michelson Interferometer).
- 5Temporal coherence refers to the phase correlation over time (related to monochromaticity and spectral linewidth). Spatial coherence refers to the phase correlation between different points in space (related to the size of the source and distance).
⚠️ Common Mistakes
- ✕Assuming two independent monochromatic laser sources are coherent; while monochromatic, their phase difference is not constant.
- ✕Confusing monochromaticity with coherence. Monochromaticity (same frequency) is a *necessary* condition for coherence but not *sufficient* on its own for independent sources.
- ✕Applying the interference intensity formula (with cos(phi) term) to incoherent sources, where the average cos(phi) over time is zero, leading to I_resultant = I_1 + I_2.
📝 Practice Questions
See allQ34.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below : (1) Both (A) and (R) are true but (R) is NOT the (2) (A) is true but (R) is false correct explanation of (A) (3) Both (A) and (R) are true and (R) is the correct (4) (A) is false but (R) is true explanation of (A)
Q41.The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is (1) 5 (2) 4 (3) 6 (4) 8
Q43.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true but (R) is not the (2) Both (A) and (R) are true and (R) is the correct correct explanation of (A) explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true
Q31.A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.] (1) 137.5 nm (2) 275 nm (3) 94.8 nm (4) 68.7 nm
Q37. Using the given P −V diagram, the work done by an ideal gas along the path ABCD is : (1) 3P0 V0 (2) −4P0 V0 (3) −3P0 V0 (4) 4P0 V0
Q29.Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be : (1) 0.23 mm (2) 0.33 mm (3) 0.63 mm (4) 0.46 mm
NCERT Chapters
- Class 12 Physics Ch 10: Wave Optics