✓ Board-verified
Physics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q18
(a) A beam of light consisting of two wavelengths 400 nm and 600 nm is used to illuminate a single slit of width 1 mm. Find the least distance of the…
A beam of light consisting of two wavelengths $\displaystyle 400$ nm and $\displaystyle 600$ nm is used to illuminate a single slit of width $\displaystyle 1$ mm. Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed $\displaystyle 1.5$ m from the slit.
In a Young's double-slit experimental set-up with slit separation $\displaystyle 0.6$ mm a beam of light consisting of two wavelengths $\displaystyle 440$ nm and $\displaystyle 660$ nm is used to obtain interference pattern on a screen kept $\displaystyle 1.5$ m in front of the slits. Find the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide.
Marking-scheme solution
At the point of coincidence for dark fringes.
$\displaystyle d \sin \theta=n \lambda_{2}=(n+1) \lambda_{1}$
$\displaystyle n \times 600=(n+1) \times 400$
$\displaystyle n=2$
Position of dark fringe from the central maxima
$\displaystyle y=\dfrac{(n+1) \lambda_{1} D}{d}$
$\displaystyle y=\dfrac{3 \times 400 \times 10^{-9} \times 1.5}{1 \times 10^{-3}}$
$\displaystyle y=1.8 \mathrm{~mm}$
Alternatively:
$\displaystyle y=\dfrac{n \lambda_{2} D}{d}$
$\displaystyle y=\dfrac{2 \times 600 \times 10^{-9} \times 1.5}{1 \times 10^{-3}}$
$\displaystyle y=1.8 \mathrm{~mm}$
At the point of coincidence for bright fringes
$\displaystyle \dfrac{n \lambda_{2} D}{d}=\dfrac{(n+1) \lambda_{1} D}{d}$
$\displaystyle n \times 660=(n+1) \times 440$
$\displaystyle n=2$
Position of bright fringe from the central maxima
$\displaystyle y=\dfrac{n \lambda_{2} D}{d}$
$\displaystyle y=\dfrac{2 \times 660 \times 10^{-9} \times 1.5}{0.6 \times 10^{-3}}$
$\displaystyle y=3.3 \mathrm{~mm}$
Alternatively:
$\displaystyle y=\dfrac{(n+1) \lambda_{1} D}{d}$
$\displaystyle y=3.3 \mathrm{~mm}$
More from Wave Optics
- Define 'wavefront' of a light wave. A plane wavefront is refracted from a convex lens. Draw the shape of the refracted wavefront. A plane wave…2025
- A double slit set-up was initially placed in a tank filled with water and the interference pattern was obtained using a laser light. When water is…2025
- The phenomenon of interference is shown by2026
- Assertion: In interference and diffraction of light, light energy reduces in one region producing a dark fringe. It increases in another region and…2024
- Using the Huygens' principle, briefly describe reflection of a plane wavefront from a reflecting surface. Hence, prove the laws of reflection.2025
- Assertion: In a Young's double-slit experiment, interference pattern is not observed when two coherent sources are infinitely close to each other.…2024
- (i) Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single…2024
- A plane wave-front propagating in a medium of refractive index ' μ_1 ' is incident on a plane surface making an angle of incidence (i). It enters…2023
CBSE Class 12 Physics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.