Identify the correct statements among the following:(A) The angular w…

The correct answer is Option (3) → (B), (C) and (D) only

Note: The given answer is as per the official NTA Answer Key. However, none of the given options appears to be correct, because statement (C) does not hold for the resolving power of a telescope, as explained below.

(A) The angular width of central maximum in a single slit diffraction pattern is directly proportional to the slit width. — Incorrect. The first minima lie at \( \sin\theta = \pm\lambda/a \), so the angular width of the central maximum, \( 2\lambda/a \), is inversely proportional to the slit width.

(B) Light waves can be polarised while sound waves can not be polarised. — Correct. Only transverse waves can be polarised. Light is transverse; sound in a gas is longitudinal.

(C) The resolving power of an astronomical telescope increases when the focal length of the objective lens is increased. — Incorrect. The smallest resolvable angle is \( \Delta\theta = 1.22\lambda/D \), where D is the diameter (aperture) of the objective; the focal length does not appear. A longer objective focal length increases the magnifying power \( f_o/f_e \), not the resolving power.

(D) Diffraction from each slit affects the interference pattern in a double slit experiment. — Correct. Each slit produces its own diffraction pattern, so the interference fringes are modulated by the single-slit diffraction envelope.

So strictly only (B) and (D) are correct, which is not among the options. NTA’s Option (3) treats (C) as correct, which holds only if magnifying power was meant.

NCERT (2026-27):
Summary – “… 5. A single slit of width a gives a diffraction pattern with a central maximum. The intensity falls to zero at angles of

    \( \displaystyle \pm\frac{\lambda}{a},\ \pm\frac{2\lambda}{a} \)

etc., with successively weaker secondary maxima in between.”

Points to Ponder – “… 4. Most interference and diffraction effects exist even for longitudinal waves like sound in air. But polarisation phenomena are special to transverse waves like light waves.”

Telescope – “… The resolving power, or the ability to observe two objects distinctly, which are in very nearly the same direction, also depends on the diameter of the objective.”

The Single Slit – “… In the double-slit experiment, we must note that the pattern on the screen is actually a superposition of single-slit diffraction from each slit or hole, and the double-slit interference pattern.”