Two slits are separated by 0.18 mm. An interference pattern is formed on a screen 80 cm away by 656.3-nm light. Calculate the fraction of the maximum intensity 0.6 cm above the central maximum.

To calculate the fraction of the maximum intensity at a certain height above the central maximum in an interference pattern, we need to understand the concept of interference and use the equation for intensity in an interference pattern.

Interference occurs when two or more waves superpose (combine) with each other. In this case, the two slits act as sources of light waves that interfere with each other on the screen, resulting in a pattern of bright and dark fringes. The central maximum is the brightest point in the pattern, where the two waves from the slits constructively interfere.

The equation for intensity in an interference pattern is given by:

I = I_max * cos^2((π * d * sinθ) / λ)

Where:
I = Intensity at a certain point in the pattern
I_max = Maximum intensity at the central maximum
d = Separation between the two slits
θ = Angle between the line joining the point and the central maximum and the perpendicular to the line between the two slits
λ = Wavelength of light

In this case, we are given that the slits are separated by 0.18 mm (0.18 x 10^-3 m), the distance to the screen is 80 cm (0.8 m), the wavelength of light is 656.3 nm (656.3 x 10^-9 m), and we want to find the intensity at a height of 0.6 cm (0.006 m) above the central maximum.

First, let's calculate the angle θ using the formula:

θ = tan^(-1)(y / D)

Where:
y = Distance above the central maximum
D = Distance between the slits and the screen

θ = tan^(-1)(0.006 / 0.8) ≈ 4.28 degrees

Now, we can substitute the given values into the equation for intensity:

I = I_max * cos^2((π * d * sinθ) / λ)

I = I_max * cos^2((π * (0.18 x 10^-3) * sin(4.28 degrees)) / (656.3 x 10^-9))

Using a calculator, evaluate the expression in the brackets:

(π * (0.18 x 10^-3) * sin(4.28 degrees)) / (656.3 x 10^-9) ≈ 1.044

Now, substitute this value into the equation:

I = I_max * cos^2(1.044)

To find the fraction of the maximum intensity, we divide the calculated intensity by the maximum intensity:

Fraction = I / I_max

Now, substitute the values to find the fraction of the maximum intensity 0.6 cm above the central maximum.