Question

Light from a 580 nm wavelength laser is shown through a double slit. This light is projected on a screen which is 4.51 m away from the slits. It is visually observed that the 12 th order maximum is missing in the pattern and this missing order is 7.76 cm from the center of the pattern.

Part A

What is the distance between the slits (center to center)?

Give your answer in millimeters.

Part B

What is the width of one of those slits?

Give your answer in millimeters.

Part C

What is the next order that is missing in the pattern?

Part D

At what distance from the center of the pattern is the missing order from part c?

Give your answer in centimeters.

Answer 1

the needed equation is Y = mLR/d---------------1

and d sin theta = mL--------------------2

where L = wavelgnth,

m = order = 1,2,3,4, ......... for brigth bands

m = 1.5, 2.5, 3.5, 4.5, ......for dark bands

R is the distance from slit to screen,

Y = distance from central spot to nth order fringe

part A :

d = n LR/Y

d = (12* 580 *10^-9 *4.51)/(0.0776)

d = 0.404 mm

---------------

part B :

d sin theta = mL

d = 1 * 580 *10^-9 *sin 90 /0.0776

d = 7.47 um

------------------------

part C:

d sin theta = nL

n = 7.47*10^-6/(580 *10^-9)

n = 13

---------------------------

part D :

Y = 13* 580 *10^-9 * 4.51/(7.47 *10^-6)

Y = 455 em