Identify the correct statement(s) among the following:
(A) The time taken by a light wave is \( 5 \times 10^{-9} \) s to travel a thickness of 1 cm of glass having refractive index 1.5.
(B) Two similar waves of amplitude of 3 mm and 5 mm reach a point in the same phase. The resultant amplitude will be 8 mm.
(C) Two waves of amplitude 2 mm each reach a point with a phase difference of \( \pi/2 \). The resultant amplitude is zero.
(D) If, one of the slits is closed in Young's double slit experiment, the interference pattern will disappear.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (D) only
(A) The time taken by a light wave is \( 5 \times 10^{-9} \) s to travel a thickness of 1 cm of glass having refractive index 1.5. — Incorrect. The speed in glass is \( c/\mu \).
\( \displaystyle t = \frac{d}{c/\mu} = \frac{\mu d}{c} = \frac{1.5 \times 10^{-2}}{3\times10^{8}} = 5\times10^{-11}\,\mathrm{s} \)
This is not \( 5\times10^{-9}\,\mathrm{s} \).
(B) Two similar waves of amplitude of 3 mm and 5 mm reach a point in the same phase. The resultant amplitude will be 8 mm. — Correct. In the same phase the amplitudes add: \( 3 + 5 = 8\,\mathrm{mm} \).
(C) Two waves of amplitude 2 mm each reach a point with a phase difference of \( \pi/2 \). The resultant amplitude is zero. — Incorrect. The resultant amplitude is not zero.
\( \displaystyle A = \sqrt{a_1^{2} + a_2^{2} + 2a_1a_2\cos\phi} = \sqrt{4 + 4 + 0} = 2\sqrt{2}\,\mathrm{mm} \)
(D) If, one of the slits is closed in Young's double slit experiment, the interference pattern will disappear. — Correct. With a single slit only one beam remains, so there is nothing to interfere; the screen shows only the diffraction pattern of one slit.
Statements (B) and (D) are correct, which is Option (3).