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Diffraction — Single slit, central maximum

Wave Optics

8

JEE Qs

8%

Hard

60

min

Thoroughly understand the conditions for minima and the unique characteristics of the central maximum (width, intensity variation) to differentiate it from interference patterns.

🧮 Key Formulas

Condition for minima: a * sin(theta_n) = n * lambda, where n = +/-1, +/-2, ...
Angular width of central maximum: 2 * theta_1 approx 2 * lambda / a (for small theta_1)
Linear width of central maximum: W = 2 * D * tan(theta_1) approx 2 * D * lambda / a (for small theta_1)
Intensity distribution: I = I_0 * (sin(beta)/beta)^2, where beta = (pi * a * sin(theta)) / lambda

✅ Key Points for JEE

  • 1The central maximum in a single-slit diffraction pattern is twice as wide as any subsequent secondary maximum or minimum fringe.
  • 2The intensity of secondary maxima decreases rapidly as the order 'n' increases; the first secondary maxima has an intensity of about 4.7% of the central maximum's intensity.
  • 3Diffraction is prominent and observable when the slit width 'a' is comparable to or slightly larger than the wavelength 'lambda' of the light.
  • 4Increasing the slit width 'a' or decreasing the wavelength 'lambda' results in a narrower central maximum and a more compact diffraction pattern.
  • 5Diffraction arises from the interference of secondary wavelets originating from different points within the *same* wavefront passing through the slit.

⚠️ Common Mistakes

  • Confusing the condition for minima in single-slit diffraction (a sin(theta) = n * lambda) with the condition for maxima in Young's Double Slit Experiment (d sin(theta) = n * lambda).
  • Incorrectly calculating the width of the central maximum as D*lambda/a instead of 2*D*lambda/a.
  • Failing to apply the small angle approximation (sin(theta) approx theta approx tan(theta)) when appropriate, or applying it when angles are not small.

📝 Practice Questions

See all

Q34.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)

2025·Assertion ReasoningMedium

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

2025·MCQMedium

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

2025·Assertion ReasoningMedium

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

2025·MCQMedium

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

2025·MCQMedium

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

2025·MCQMedium

NCERT Chapters

  • Class 12 Physics Ch 10: Wave Optics