Using light from a monochromatic source to study diffraction in a single slit of width 0.1 mm, the linear width of central maxima is measured to be 5 mm on a screen held 50 cm away. The wavelength of light used is _______________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 5 \times 10^{-7}\,\mathrm{m} \)
In single-slit diffraction the first minima lie at angles \( \theta = \pm\lambda/a \), so the central maximum spreads over \( 2\lambda/a \). On a screen at distance \( D \) its linear width is
\( \displaystyle w = \frac{2 \lambda D}{a} \;\Rightarrow\; \lambda = \frac{w\,a}{2D} \)
\( a = 0.1\,\mathrm{mm} = 1\times10^{-4}\,\mathrm{m} \)
\( w = 5\,\mathrm{mm} = 5\times10^{-3}\,\mathrm{m} \)
\( D = 50\,\mathrm{cm} = 0.5\,\mathrm{m} \)
\( \displaystyle \lambda = \frac{5\times10^{-3} \times 1\times10^{-4}}{2 \times 0.5} = 5\times10^{-7}\,\mathrm{m} \)