Question

Monochromatic light with a wavelength of 6.4 E -7 meter passes through two narrow slits, producing an interference pattern on a screen 4.0 meters away. The first order bright band lines are 2.0 E -2 meters away from the central bright maxima. What is the distance between the slits?
1.3 E -4 m
8.0 E -6 m
3.2 E -9 m
7.8 E3 m

Answer 1

Answer:

The distance between the slits is given by  1.3 × $10^{-4}$ m

Given:

$\lambda = 6.4 \times 10^{-7} m$

D = 4 m

y = $2 \times 10^{-2} m$

m = 1

To find:

distance between slits, d = ?

Formula used:

y = $\frac{m \times \lambda \times D}{d}$

y = distance of first bright band from central maxima

D = distance between screen and source

d = distance between slits

$\lambda$ = wavelength

Solution:

distance of first bright band from central maxima is given by,

y = $\frac{m \times \lambda \times D}{d}$

y = distance of first bright band from central maxima

D = distance between screen and source

d = distance between slits

$\lambda$ = wavelength

Thus,

d = $\frac{m \times \lambda \times D}{y}$

d = $\frac{1 \times 6.4 \times 10^{-7} \times 4 }{2 \times 10^{-2} }$

d = 1.28 × $10^{-4}$

d = 1.3 × $10^{-4}$ m

The distance between the slits is given by  1.3 × $10^{-4}$ m