Read the following passage and answer the questions.
A student studies diffraction at a single slit. She uses a laser that gives light of wavelength 600 nm. The beam falls normally on a narrow slit. The width of the slit can be changed with a screw. A white screen is placed 1.0 m behind the slit. With the slit width set at 0.2 mm, she sees a broad bright band at the centre of the screen. On both sides of it there are dark and bright bands. She marks the centre of each band with a pencil. Later she changes the slit width, the wavelength and the screen distance, and notes how the bands move.
At home she tries a simpler version. She holds two razor blades with their edges parallel, so that a narrow slit is left between them. Through this slit she looks at a clear glass bulb with a straight filament. She keeps the slit parallel to the filament and close to her eye.
In the laser set-up, only the change given in List-I is made each time. Match List-I with List-II.
| List-I (change in the laser set-up) | List-II (distance of the first dark band from the centre) |
|---|---|
| (A) The slit width is doubled | (I) Becomes two-thirds |
| (B) The screen is moved to twice its distance from the slit | (II) Becomes half |
| (C) The wavelength is changed from 600 nm to 400 nm | (III) Remains the same |
| (D) The slit width and the wavelength are both doubled | (IV) Becomes double |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
The first dark band is at the angle \( \theta=\lambda/a \). On a screen at distance \( D \), its distance from the centre is \( y_1=\lambda D/a \). So \( y_1 \) grows with \( \lambda \) and \( D \), and falls as \( a \) grows.
(A) The slit width is doubled — This matches (II) Becomes half. \( y_1 \) varies as \( 1/a \), so doubling \( a \) halves it.
(B) The screen is moved to twice its distance from the slit — This matches (IV) Becomes double. \( y_1 \) varies as \( D \).
(C) The wavelength is changed from 600 nm to 400 nm — This matches (I) Becomes two-thirds. \( y_1 \) varies as \( \lambda \), and \( 400/600=2/3 \).
(D) The slit width and the wavelength are both doubled — This matches (III) Remains the same. The ratio \( \lambda/a \) does not change, so the band stays where it was.
NCERT (2026-27):
The single slit – “… The minima (zero intensity) are at \( \theta\approx n\lambda/a \), n = ±1, ±2, ±3, ….”