Question

Monochromatic light falls on two very narrow slits 0.044 mm apart. Successive fringes on a screen 6.40 maway are 8.1 cm apart near the center of the pattern. Determine the wavelength of the light.
Express your answer to two significant figures and include the appropriate units
Determine the frequency of the light.
Express your answer to two significant figures and include the appropriate units

Answer 1

Answer:

The wavelength is $5.57\times10^{-7}\ m$

The frequency is $5.4\times10^{14}\ Hz$

Explanation:

Given that,

Distance between slits d= 0.044 mm

Distance between fringe and center of the pattern y= 8.1 cm

Distance between slits and fringes D = 6.40 m

We need to calculate the wavelength

For constructive interference

$d\sin\theta=n\lambda$

$y=D\tan\theta$

$y=D\dfrac{m\lambda}{d}$

$\lambda=\dfrac{dy}{Dm}$

Put the value into the formula

$\lambda=\dfrac{0.044\times10^{-3}\times8.1\times10^{-2}}{6.40\times1}$

$\lambda=5.57\times10^{-7}\ m$

We need to calculate the frequency

Using formula of frequency

$f =\dfrac{c}{\lambda}$

$f=\dfrac{3\times10^{8}}{5.57\times10^{-7}}$

$f=5.4\times10^{14}\ Hz$

Hence, The wavelength is $5.57\times10^{-7}\ m$

The frequency is $5.4\times10^{14}\ Hz$