Question

A double slits separated by 0.0580 mm is located at a distance of 1.50 m from a screen. (a) If yellow light of wavelength 588 nm strikes the double slit, what is the separation between the first-order and third-order dark fringes on the screen

Answer 1

Answer:

The separation between third order and first order is 0.0304 m

Explanation:

Given:

Separation between two slit $d = 0.0580 \times 10^{-3}$ m

Distance between slit and screen $D = 1.50$ m

Wavelength of light $\lambda = 588 \times 10^{-9}$ m

From the formula of interference of light,

    $d \sin \theta = n\lambda$

Here $\sin \theta = \frac{x}{D}$

 $\frac{dx}{D} = n \lambda$

   $x = \frac{n\lambda D}{d}$

Where $x =$ separation between fringes

Here we have to find between third order and first order,

   $x = \frac{(n_{3} - n_{1})\lambda D }{d}$

Where $n_{3}$ = 3   $n_{1}$ = 1

   $x = \frac{2 \times 588 \times 10^{-9} \times 1.50}{0.0580 \times 10^{-3} }$

   $x = 0.0304$ m

Therefore, the separation between third order and first order is 0.0304 m