Question

(1)(A) Young's double slit experiment is one of the quintessential experiments in physics. The availability of low cost lasers in recent years allows us to perform the double slit experiment rather easily in class. Your professor shines a green laser (566 nm) on a double slit with a separation of 0.106 mm. The diffraction pattern shines on the classroom wall 4.0 m away. Calculate the fringe separation between the fourth order and central fringe.

(B)Working in lab class you shine a green laser (5.65 10² nm) onto a double slit with a separation of 0.280 mm. What is the distance between the first and second dark fringe that shines on the wall 2.20 m away?

(C)You shine an orange laser (587 nm) on a double slit in an experiment you perform in your physics lab. Measuring with a protractor you see that the interference pattern makes the first fringe at 11.0° with the horizontal. What is the separation between the slits?

(D)What is the separation between two slits for which 650 nm light has its first minimum at an angle of 31.5°?

Answer 1

(1)

(A) Fringe with = Distance between two consecutive bright fringes = y = D / d,

where, D = Distance between the screen and the slits = 4 m,

d = Slit seperation = 0.106 mm = 1.06 x 10^-4 m,

and, = Wavelength of the light used = 566 nm = 5.66 x 10^-7 m.

Hence, y = ( 4 x 5.66 x 10^-7 ) / ( 1.06 x 10^-4 ) m ~ 2.136 x 10^-2 m.

Hence, the fringe separation between the fourth order and central fringe is :

4y = 4 x 2.136 x 10^-2 m = 8.544 x 10^-3 m = 8.544 mm.

(B) Fringe with = Distance between two consecutive dark fringes = y = D / d,

where, D = Distance between the screen and the slits = 2.2 m,

d = Slit seperation = 0.28 mm = 2.8 x 10^-4 m,

and, = Wavelength of the light used = 565 nm = 5.65 x 10^-7 m.

Hence, y = ( 2.2 x 5.65 x 10^-7 ) / ( 2.8 x 10^-4 ) m ~ 4.44 x 10^-3 m.

Hence, the distance between the first and second dark fringe is : y = 4.44 x 10^-3 m = 4.44 mm.