Question

Two slits illuminated with red light of wavelength 800 nm, slits have a separation of 1 mm, Fringe pattern is observed on a screen at 1 metre from plane of slits. The distance between 3rd maxima and 7th minima is

• A. 2.8 mm
• B. 4.2 mm
• C. 5.6 mm
• D. 1.4 mm

Answer 1

The correct option is A 2.8 mm

$Y_{3rdbright}=3\beta =\frac{3D\lambda }{d}$
$Y_{7thminima}=(2n-1)\frac{D\lambda }{2d}$ = $\frac{13D\lambda }{2d}$
Gap = $Y_{7thmin}-Y_{3rdbright}$
$=\frac{13D\lambda }{2d}-\frac{3D\lambda }{d}=\frac{7D\lambda }{2d}=\frac{7}{2}\times \frac{1\times 800\times {10}^{-9}}{{10}^{-3}}$
$\frac{7}{2}\times 8\times {10}^{-4}$
$28\times {10}^{-4}$
= 2.8 mm