Two very narrow slits are spaced `1.80 mu`m apart and are placed 35.0 cm from a screen. What is the distance between the first and second dark lines of the interference pattern when the slits are illuminated with coherent light of `lambda = 550nm ?` (Hint : The angle `theta` is not small).

Explanation

`d sin theta_1 = lambda/2 `
` sin theta_1 = lambda/(2d) = (550 xx 10^(-9))/(2 xx 1.8 xx 10^-6)`
` :. theta_1 = 8.78^@ `
` y_1/D = tan theta_1`
` :. Y_1 = D tan theta_1 `
`= 35 tan 8.78^@`
= 5.41 cm
`d sin theta_2 = (3lambda)/2`
` :. sin theta_2 = (3lambda)/(3d) = (3 xx 550 xx 10^-9)/(2xx 1.8 xx 10^-6)`
` :. theta_2 = 27.27^@`
` :. y_2 = D tan theta_2`
` = 35tan 27.27^@`
= 18cm
` Deltay = y_2 - y_1 = 12.6 cm.