In a double-slit experiment the distance between slits is 5.6 mm and the slits are 0.81 m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 410 nm, and the other due to light of wavelength 660 nm. What is the separation in meters on the screen between the m

The separation in meters on the screen between the bright fringes of the two interference patterns is 1.08 × 10⁻⁴ m

Explanation:

Here is the complete question:

In a double-slit experiment, the distance between slits is 5.6 mm and the slits are 0.18 m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 410 nm, and the other due to light of wavelength 660 nm. What is the separation in meters on the screen between the third-order (m = 3) bright fringes of the two interference patterns?

Explanation:

For a bright fringe, the distance of the bright fringe can be determined from

Where is the order

is the wavelength

is the distance from the screen

is the distance between the slits

From the question,

= 5.6 mm = 5.6 × 10⁻³ m

= 0.81 m

m = 3

For the first interference pattern, = 410 nm = 410 × 10⁻⁹ m

∴ becomes

m

For the second interference pattern, = 660 nm = 660 × 10⁻⁹ m

∴

m

Now, the separation between the bright fringes of the two interference patterns will be the difference in the distances of the bright fringes for the two interference patterns. That is

2.86 × 10⁻⁴ m - 1.78 × 10⁻⁴ m = 1.08 × 10⁻⁴ m

Hence, the separation in meters on the screen between the bright fringes of the two interference patterns is 1.08 × 10⁻⁴ m.

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