Question

Two slits separated by a distance of 1 mm are illuminated with red light of wavelength $6.5 ? 10^{-7}\, m$. The interference fringes are observed on a screen placed 1 m from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to

• A. 0.65 mm
• B. 1.63 mm
• C. 3.25 mm
• D. 4.88 mm

Answer 1

The Correct Option is B

Here, $d=1\,mm=10^{-3}\,m, \lambda=6.5\times10^{-5}\,m$ $D=1\,m$ $x_{5}=n\lambda \frac{D}{d}=5\times6.5\times10^{-7}\times\frac{1}{10^{-3}}=32.5\times10^{-5}\,m$ $x_{3}=\left(2n-1\right) \frac{\lambda}{2} \frac{D}{d}=\frac{\left(2\times3-1\right)\times6.5\times10^{-7}\times1}{2\times10^{-3}}$ $=16.25\times10^{-4}\,m$ $x_{5}-x_{3}=\left(32.5-16.25\right) \times10^{-4}\,m =16.25\times10^{-4}m=1.63mm$