Question

In a young’s double slit arrangement, two very narrow slits are spaced $d=1.8\mu m$ apart and are placed D = 35 cm from a screen. The arrangement is illuminated with coherent light with wavelength $\lambda =540nm$. Choose the correct statement(s)

• A. The distance between the second dark lines on either sides of the central bright line in the interference pattern is 40.4 cm.
• B. The distance between the second dark lines on either sides of the central bright line in the interference pattern is 31.5 cm.
• C. The total number of dark fringes seen on the screen is 36.
• D. The value of $\frac{\lambda }{d}=\frac{1}{3}$

Answer 1

Answer: (B), (C)

The correct options are
B The distance between the second dark lines on either sides of the central bright line in the interference pattern is 31.5 cm.
C The total number of dark fringes seen on the screen is 36.

$\Delta x=dsin\theta$. In this case '$\theta$' is not small
$\therefore 2^{nd}$ dark $sin{\theta }_2=\frac{3\lambda }{2d}=\frac{11}{24}$
$tan\theta =\frac{x}{D}\Rightarrow x=Dtan\theta =35\times \frac{11}{21.3}=18$
$\therefore 2x=36$