In a Young's double-slit experiment, the slits are separated by 0.28 mm and the wavelength of light used is \( 6000\,\mathring{\mathrm{A}} \). The fringes are observed on a screen placed 1.4 m away from the slits. The distance between the central bright fringe and the fourth bright fringe will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.2 cm
In Young's double-slit experiment the fringe width is \( \beta = \lambda D/d \). The \( n \)th bright fringe from the centre is at \( y_n = n\beta \).
\( \lambda = 6000\,\mathring{\mathrm{A}} = 6\times10^{-7}\,\mathrm{m} \)
\( d = 0.28\,\mathrm{mm} = 2.8\times10^{-4}\,\mathrm{m} \)
\( D = 1.4\,\mathrm{m} \)
\( \displaystyle \beta = \frac{6\times10^{-7}\times1.4}{2.8\times10^{-4}} = 3\times10^{-3}\,\mathrm{m} = 0.3\,\mathrm{cm} \)
\( \displaystyle y_4 = 4\beta = 4\times0.3 = 1.2\,\mathrm{cm} \)