A single slit of width $0.05,\text{mm}$ is illuminated by monochromatic light of wavelength $700,\text{nm}$. The screen is placed $3.0,\text{m}$ behind the slit. Determine the linear width $w$ of the central bright fringe on the screen.

Step-by-step solution

1. Central maximum width formula: $w=\frac{2Llambda}{a}$ where $L=3.0,\text{m}$, $\lambda =700\times 10^{-9},\text{m}$, $a=0.05\times 10^{-3},\text{m}$.
2. Compute numerator: $2Llambda=2\times 3.0\times 700\times 10^{-9}=4.2\times 10^{-6},{\text{m}}^2$.
3. Divide by $a$: $w=\frac{4.2\times 10^{-6}}{0.05\times 10^{-3}}=8.4\times 10^{-2},\text{m}$.
4. Convert to centimetres: $8.4\times 10^{-2},\text{m}=8.4,\text{cm}$.

Concept tested: Single‑slit central maximum width

Published 13 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked