Match List-I with List-II
| List-I | List-II | ||
| Physical quantity | Formula | ||
| (A) | Width of a central maximum | (I) | \( 2\lambda/a \) |
| (B) | Fringe width | (II) | \( a^{2}/\lambda \) |
| (C) | Fresnel's distance | (III) | \( 2D\lambda/a \) |
| (D) | Angular spread of central maximum | (IV) | \( D\lambda/d \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (III), (B) - (IV), (C) - (II), (D) - (I)
In single-slit diffraction of slit width \( a \) with the screen at distance \( D \), the central maximum spreads between the first minima on either side, where \( \sin\theta = \pm\lambda/a \). In Young's double-slit experiment the slit separation is \( d \).
(A) Width of a central maximum — this matches (III) \( 2D\lambda/a \). The linear width on the screen is \( 2D\tan\theta \approx 2D\lambda/a \).
(B) Fringe width — this matches (IV) \( D\lambda/d \). This is the fringe width \( \beta \) of the double-slit pattern.
(C) Fresnel's distance — this matches (II) \( a^{2}/\lambda \). It is the distance up to which the spreading of the beam by diffraction is smaller than the size \( a \) of the aperture, so ray optics holds.
(D) Angular spread of central maximum — this matches (I) \( 2\lambda/a \). The angle between the two first minima is \( 2\theta \approx 2\lambda/a \).