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Two coherent sources are 0.3 mm apart. They are 0.9 m away from the screen. The second dark fringe is at a distance of 0.3 cm from the centre. Find the distance of fourth bright fringe from the centre. Also, find the wavelength of light used.

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0.8 cm , $6.67 \times 10^{- 7}$ m

0.4 cm , $5.75 \times 10^{2}$ m

0.9 cm, $5.65 \times 10^{3}$ m

o.5 cm , $6.61 \times 10^{- 7}$ m

answer is B.

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Detailed Solution

Given,. $d = 0.3 \times 10^{- 3} m$ ,D=0.9 m

$\frac{3 λ D}{2 d} = 0.3 \times 10^{- 2} c m$

$\frac{λ D}{d} =$ $(0.3 \times 10^{- 2})$ $(\frac{2}{3})$

$= 0.2 \times 10^{- 2}$ m $= 0.2$ cm

Distance of fourth bright fringe from centre $= \frac{4 λ D}{d}$ $= 0.8 c m$

$λ = (\frac{d}{D})$ $(0.2 \times 10^{- 2}) m$ $= (\frac{0.3 \times 10^{- 3}}{0.9})$ $(0.2 \times 10^{- 2})$

$= 6.67 \times 10^{- 7} m$

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