Question

Two slits separated by a distance of $1mm$ are illuminated by light of wavelength ${6.510}^{7}m$. Interference fringes are observed on a screen placed at a distance of $1m$ from the slits. Calculate the distance between the third dark fringe and fifth bright fringe.

• A. $0.65mm$
• B. $1.62mm$
• C. $3.25mm$
• D. $4.88mm$

Answer 1

Answer: (C)

$3.25mm$

Given,

Distance between two slit(d)$=1mm=1\times {10}^{-3}m$

Wave length of light $\lambda =6.5\times {10}^{-7}m$

Distance between screen and slit is $D=1m$

We know that

Distance of dark fringe is $y=(2n-1)\lambda D$

Distance of Bright fringe is $y=\frac{n\lambda D}{d}$

Distance between third dark and fifth bright fringe is

$y_5-y_3=\frac{n\lambda D}{d}-(2n-1)\lambda D$

Substitute all value in above equation

$y_5-y_3=\frac{5\times 6.5\times {10}^{-7}\times 1}{1\times {10}^{-3}}-(2\times 3-1)6.5\times {10}^{-7}\times 1=32.5\times {10}^{-4}-32.5\times {10}^{-7}=3.25\times {10}^{-3}-0.00325\times {10}^{-3}=3.25mm$

Correct option is C.