CBSE Class 12 Physics Interference of Light Solved Examples

CBSE Class 12 Physics Interference of Light Solved Examples. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

Ex.1 Consider interference between waves from two sources of Intensites I & 4I. Find intensities at points where the phase difference is π.
(A) I (B) 5I (C) 4I (D) 3I
Sol. I = R² = a₁ ² + a₂ ² + 2a₁ a₂ cos δ = I + 4I + 4I cos π I = 5I – 4I = I

Ex.2 The width of one of the two slits in a Young's double slit experiment is double of the other slit. Assuming that the amplitude of the light coming from a slit is proportional to slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.
(A) 34 : 1 (B) 9 : 1 (C) 4 : 1 (D) 16 : 1
Sol. Suppose the amplitude of the light wave coming from the narrower slit is A and that coming from the wider slit is 2A. The maximum intensity occurs at a place where constructive interference takes place. Then the resultant amplitude is the sum of the individual amplitudes. Thus, Amax = 2A + A = 3A The minimum intensity occurs at a place where destructive interference takes place. The resultant amplitude is then difference of the individual amplitudes.

Ex.3 The intensity of the light coming from one of the slits in a young's double slit experiment is double the intensity from the other slit. Find the ratio of the  maximum intensity to the minimum intensity in the interference fringe pattern observed.
(A) 9 : 1 (B) 34 : 1 (C) 4 : 1 (D) 16 : 1

Ex. 5 The equation of two light waves are y1 = 6coswt, y2 = 8cos(wt + φ). The ratio of maximum to minimum intensities produced by the superposition of these waves will be
(A) 49 : 1 (B) 1 : 49 (C) 1 : 7 (D) 7 : 1

Ex. 6 In a Young's slit experiment, the separation between the slits is 0.10 mm, the wavelength of light used is 600 nm and the interference pattern is observed on a screen 1.0 m away.Find the separation between the successive bright fringes.
(A) 6.6 mm (B) 6.0 mm (C) 6 m (D) 6 cm.
Sol. The separation between the sucessive bright fringes is-
β =Dλ/d
β = 6.0 mm.

Ex. 7 Two waves originating from source S1 and S2 having zero phase difference and common wavelength λ will show completely destructive interference at a point P if (S1 P – S2 P) is- [MP PMT, 87]
(A) 5λ (B) 3λ/4 (C) 2λ (D) 11λ/2

Ex. 9 In Young's experiment the wavelength of red light is 7.5 × 10–5 cm. and that of blue light 5.0 × 10–5 cm. The value of n for which (n + 1)th the blue bright band coincides with nth red band is-
(A) 8 (B) 4 (C) 2 (D) 1

Ex. 10 In Young's double slit experiment, carried out with light of wavelength λ = 5000 Aº, the distance between the slits is 0.2 mm and the screen is at 200 cm from the slits. The central maximum is at x = 0. The third maximum will be at x equal to.
(A) 1.67 cm (B) 1.5 cm (C) 0.5 cm (D) 5.0 cm.

Ex. 11 Two slits separated by a distance of 1mm are illieminated with red light of wavelength 6.5 × 10-7 m. The interference fringes are observed on a screen placed 1m from the slits. The distance between third dark fringe & the fifth bright fringe is equal to.
(A) .65 mm (B) 1.63 mm (C) 3.25 mm (D) 4.87 mm.
Sol. β =λD/d = 3= 6.5 ×10^-7 ×1
β = .65 × 10^–3 m = .65 mm
The distance between fifth bright fringe from third dark fringe = 2.5 β=2.5×.65 = 1.63 mm.
Ex. 12 In an experiment the two slits are 0.5 mm apart and the fringes are observed to 100 cm from the plane of the slits. The distance of the 11th bright fringe from the Ist bright fringe is 9.72 mm. Calculate the wavelength.
(A) 4.85 × 10^–5 cm (B) 4.85 × 10^–5 m (C) 4.86 × 10^–7 m (D) 4.86 × 10^–5 cm

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