Question

Two slits separated by a distance of 1 mm are illuminated with red light of wavelength $6.5\times {10}^{-7}$ meter. The interference fringes are observed on a screen placed one meter from the slits. The distance between the third dark fringe and fifth bright fringe (excluding central bright)on the same side of center is equal to

• A. 0.65 mm
• B. 1.63 mm
• C. 3.25 mm
• D. 4.8 mm

Answer 1

The correct option is B 1.63 mm

For dark fringes,
$y_n=(2n-1)\frac{\lambda D}{2d}\Rightarrow Y_3=\frac{5}{2}\frac{\lambda D}{d}$
For bright fringes,
$y_n=\frac{n\lambda D}{d}\Rightarrow Y_5=\frac{5\lambda D}{d}Y=Y_5-Y_{3}Y=\frac{5\lambda }{2}\frac{D}{d}=\frac{5\times 6.5\times {10}^{-7}\times 1}{2\times {10}^{-3}}=1.625\times {10}^{-3}m=1.63mm$