Question

Light with a wavelength of 410 nm (4.1 x 10-7 m) is incident upon a double slit with a separation of 0.6 mm (6 x 10-4 m). A screen is location 3.6 m from the double slit. (a) At what distance from the center of the screen will the first bright fringe beyond the center fringe appear?

Answer 1

2.4599×10⁻³ m

Step-by-step explanation:

The relation between the distance of the slits and the angle through which it is passed is:

dsinθ=nλ

where,

n can be any integer

d is the distance between the two slits

λ is the wavelength of light.

Since for the first bright fringe, n=1

The experiment scenario can be drawn with the help of an image shown below.

Given:

d = 6×10⁻⁴ m

λ = 4.1×10⁻⁷ m

6×10⁻⁴×sinθ=(1) 4.1×10⁻⁷

sinθ = 6.8333×10⁻⁴

Since sinθ is very small, so, sinθ = tanθ

tanθ = 6.8333×10⁻⁴

Distance between slit and screen = 3.6 m

So,

tanθ = (The distance if the first bright fringe)/(Distance between slit and screen)

The distance if the first bright fringe = 6.8333×10⁻⁴×3.6 m = 2.4599×10⁻³ m