Posted by **Jim** on Friday, March 30, 2012 at 1:23pm.

Light waves with two different wavelengths, 632 nm and 474 nm, pass simultaneously through a single slit whose width is 7.63 x 10-5 m and strike a screen 1.30 m from the slit. Two diffraction patterns are formed on the screen. What is the distance (in cm) between the common center of the diffraction patterns and the first occurrence of the spot where a dark fringe from one pattern falls on top of a dark fringe from the other pattern?

- Physics help please! -
**Elena**, Friday, March 30, 2012 at 4:39pm
Lets use the condition of diffraction minimum for one split of the width b

bsinα =k1λ1

bsinα =k2λ2,

Since we have superposition of two maxima

bsinα is the same for two wavelengths,

k1λ1= k2λ2,

λ1/λ2 = k1/k2, 632/474 = 4/3.

Therefore k1=4, k2=3.

Now

sinα = k1λ1/b =463210^-9/ 7.6310^-5 =0.033.

As the angle is very small tanα = sinα = 0.033.

tan α= x/L,

x =L tanα =1.30.033 = 0.043 m = 4/3 cm

- Physics help please! -
**Elena**, Saturday, March 31, 2012 at 6:01pm
My mistake.

It should be

k1λ1= k2λ2,

λ1/λ2 = k2/k1, 632/474 = 4/3.

k1 =3 k2 = 4

sinα = k1λ1/b =363210^-9/ 7.6310^-5 =0.0248

x=L tanα =L sinα =1.30.0248 =0.0323 m = 3.23 cm

## Answer This Question

## Related Questions

- Physics - Light waves with two different wavelengths, 632 nm and 474 nm, pass ...
- Physics - Light waves with two different wavelengths, 632 nm and 474 nm, pass ...
- physics - A flat screen is located 0.43 m away from a single slit. Light with a ...
- physics - single-slit diffraction pattern is formed when light of 680.0 nm is ...
- Physics 2 - Light with λ = 530 nm passes through a single slit and then ...
- physics - In a double-slit experiment, two beams of coherent light traveling ...
- Physics - In a single-slit diffraction pattern on a flat screen, the central ...
- Physics - Light of a red laser (wavelength λ=650 nm) goes through a narrow ...
- physics - Light shines through a single slit whose width is 1.12 mm. A ...
- Physics - Light shines through a single slit whose width is 1.12 mm. A ...

More Related Questions