Problem 17.8


Light from a sodium lamp (wavelenght = 589) illuminates two narrow slits. The fringe spacing on a screen 150 cm behind the slits is 4.0 mm .



Part A -

What is the spacing (in mm ) between the two slits?

Express your answer using two significant figures.

To find the spacing between the two slits, we can use the formula for fringe spacing in a double-slit interference pattern:

d*sin(θ) = m*λ

where d is the spacing between the two slits, θ is the angle of the observed fringe, m is the order of the fringe, and λ is the wavelength of the light.

In this case, we are given the fringe spacing (4.0 mm) and the wavelength of the light (589 nm). We need to convert the wavelength to meters before performing the calculation.

1 nm = 1 x 10^-9 m

Therefore, the wavelength of the light is 589 x 10^-9 m.

We can rearrange the formula to solve for d:

d = (m*λ) / sin(θ)

Since no specific order m or angle θ is given in the problem, we can assume that we are looking at the central maximum where m = 0 and sin(θ) = 1.

Plugging in the values into the formula:

d = (0 * 589 x 10^-9 m) / 1

Simplifying the equation:

d = 0

Accordingly, the spacing between the two slits is 0 mm.

To find the spacing between the two slits, we can use the formula:

d = λL / y

where:
d is the spacing between the two slits
λ is the wavelength of the light source
L is the distance between the slits and the screen
y is the fringe spacing on the screen

Given:
λ = 589 nm = 0.589 μm
L = 150 cm = 1500 mm
y = 4.0 mm

Substituting the values into the formula, we get:

d = (0.589 μm * 1500 mm) / 4.0 mm

Simplifying the equation, we get:

d = 220.875 μm

Therefore, the spacing between the two slits is approximately 220.88 μm or 220.88 mm (rounded to two significant figures).