Light from sodium lighting passes through a single slit, then through double slit system and is projected on a screen. The separation distance between the slits of the double slits is 1.00mm. The screen is placed at 1.0m from the double slits system and the sodium light lighting has a wavelength of 5.9x10-5cm

a)Calculate the separation distance between two consecutive bright fringes on the screen.(0.59mm)
b)If the sodium lighting is replaced with a BLUE monochromatic source, what will happen to the image pattern on the screen?

To calculate the separation distance between two consecutive bright fringes on the screen, we can use the equation:

d*sin(theta) = m * lambda

Where:
- d is the separation distance between the double slits (1.00 mm in this case)
- theta is the angle of diffraction of the bright fringe
- m is the order of the bright fringe (1 for the first order, 2 for the second order, etc.)
- lambda is the wavelength of the sodium lighting (5.9x10^-5 cm in this case)

a) Let's calculate the separation distance between two consecutive bright fringes using the formula mentioned above:

Using the given values:
- d = 1.00 mm = 0.1 cm
- lambda = 5.9x10^-5 cm

We can rearrange the formula to solve for theta:

theta = arcsin(m * lambda / d)

For the first-order bright fringe (m = 1):

theta = arcsin(1 * 5.9x10^-5 cm / 0.1 cm)

Now, we can calculate the angle:

theta ≈ 0.059 radians

To find the separation distance between two consecutive bright fringes on the screen, we can use the approximation:

Separation distance = m * wavelength * screen distance / d

For the first-order bright fringe (m = 1):

Separation distance ≈ 1 * 5.9x10^-5 cm * 100 cm / 0.1 cm
Separation distance ≈ 0.59 cm ≈ 0.59 mm

Therefore, the separation distance between two consecutive bright fringes on the screen is approximately 0.59 mm.

b) If the sodium lighting is replaced with a BLUE monochromatic source, the wavelength will be different. The wavelength of blue light is generally shorter than that of sodium light. As a result, the diffraction pattern on the screen will change. The bright fringes will be closer together because the smaller wavelength leads to a larger angle of diffraction.

In summary, if the sodium lighting is replaced with a blue monochromatic source, the separation distance between the consecutive bright fringes on the screen will decrease compared to the previous case with sodium lighting.