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In Young’s double slit experiment the separation d between the slits is 2mm, the wavelength $λ$ of the light used is 5896A⁰ and distance D between the screen and slits is 100cm. It is found that the angular width of the fringes is 0.20⁰. To increase the fringe angular width to 0.210 (with same $λ$ and D) the separation between the slits needs to be changed to

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1.8 mm

1.7 mm

2.1 mm

1.9 mm

answer is B.

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Detailed Solution

$\begin{array}{l} δ = \frac{B}{D} = \frac{λ}{d} \\ \frac{δ_{1}}{δ_{2}} = \frac{d_{2}}{d_{1}}; d_{2} = \frac{δ_{1} d_{1}}{δ_{2}} = \frac{0 .2}{0 .21} \times 2 \\ d_{2} = \frac{20 \times 2}{21} = \frac{40}{21} = 1 .9 mm \end{array}$

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