In a diffraction pattern due to a narrow slit of width a, alternate dark and bright fringe pattern is obtained on a screen kept at distance D from the slit. Choose the correct option.
(A) The angular width of central maximum is given by \( 2D/a \), linear width is given by \( 2D\lambda/a \).
(B) When the size of aperture, a is quite large, the diffraction effect is negligible.
(C) For light of smaller wavelength, angular width of central maximum increases, while linear width decreases.
(D) Angular width of central maximum does not decrease while linear width decreases on decreasing distance of screen from slit.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
For a single slit, the central maximum has angular width \( 2\lambda/a \) and linear width \( 2D\lambda/a \).
(A) The angular width of central maximum is given by \( 2D/a \), linear width is given by \( 2D\lambda/a \). — Incorrect. The angular width is \( 2\lambda/a \); \( 2D/a \) has no wavelength and is not even an angle.
(B) When the size of aperture, a is quite large, the diffraction effect is negligible. — Correct. For \( a \gg \lambda \) the spreading \( \lambda/a \) is tiny and light travels in straight lines.
(C) For light of smaller wavelength, angular width of central maximum increases, while linear width decreases. — Incorrect. Both \( 2\lambda/a \) and \( 2D\lambda/a \) decrease when \( \lambda \) decreases.
(D) Angular width of central maximum does not decrease while linear width decreases on decreasing distance of screen from slit. — Correct. The angular width \( 2\lambda/a \) does not contain \( D \), but the linear width \( 2D\lambda/a \) is proportional to \( D \).
Statements (B) and (D) are correct, which is Option (4).