Young's Double Slit Experiment — Fringe width, conditions
Wave Optics
8
JEE Qs
8%
Hard
60
min
Master the concept of path difference and phase difference, as it's the core to solving complex problems involving modifications to the YDSE setup.
🧮 Key Formulas
✅ Key Points for JEE
- 1Fringe width (β) is directly proportional to the wavelength (λ) and screen distance (D), and inversely proportional to the slit separation (d).
- 2The central fringe (n=0) is always bright, corresponding to zero path difference (Δx=0) and maximum intensity.
- 3If the YDSE setup is immersed in a medium of refractive index μ, the wavelength of light changes to λ' = λ/μ, and consequently, the fringe width becomes β' = β/μ.
- 4If a thin transparent sheet of thickness 't' and refractive index 'μ_f' is placed in front of one slit, the optical path from that slit increases by (μ_f - 1)t, causing a shift in the central bright fringe. The shift is given by Δy = [(μ_f - 1)tD]/d.
- 5For sustained interference patterns, the two sources must be coherent (maintain a constant phase difference) and monochromatic (single wavelength).
⚠️ Common Mistakes
- ✕Incorrectly identifying the 'n' value for dark fringes (e.g., confusing 'n' for n-th dark fringe with the 'n' in the formula (n + 1/2)λ).
- ✕Forgetting to adjust the wavelength (λ) when the YDSE experiment is performed in a medium other than air/vacuum.
- ✕Miscalculating the shift of the central maximum due to a thin film, especially when one considers the absolute refractive index or relative refractive index incorrectly.
- ✕Confusing the slit separation 'd' with the slit-to-screen distance 'D' in the formulas.
📝 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