Question

Parallel rays of monochromatic light with wavelength 576 nm illuminate two identical slits and produce an interference pattern on a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm.

If the intensity at the center of the central maximum is 4.00×10⁻⁴ W/m2 , what is the intensity at a point on the screen that is 0.900 mm from the center of the central maximum?

Express your answer to three significant figures and include the appropriate units.

NOTE: The last answer I got was I=2.76*10^-6 W/m^2 and it was incorrect. HELP!

Answer 1

Y = position relative to center = 0.9 mm

D = screen distance = 750 m

d = slit width = 0.64 x 10^-3 m

w = width of slit = 0.434 x 10^-3

Sin = tan = Y/D = 0.9/750 = 1.2 x 10^-3

intensity is given as

I = I_o Cos²(/2) Sin(/2)//2)²

where

/(2) = d Sin/

/(2(3.14)) = (0.64 x 10^-3 ) (1.2 x 10^-3)/(576 x 10^-9)

= 8.4

and

/(2) = w Sin/

/(2(3.14)) = (0.434 x 10^-3 ) (1.2 x 10^-3)/(576 x 10^-9)

= 5.68

I = I_o Cos²(/2) Sin(/2)//2)²

I =(4 x 10^-4)Cos²(8.4/2) Sin(5.68/2)/5.68/2)2

I = 1.05 x 10^-6