A student investigates the interference of light in a Young’s double slit experiment.

i). Explain why there is no interference pattern if the two slits are 5.0 cm apart.
ii). Explain why it is better for the student to observe the interference patterns at a distance of about 1.0 m from the slits.

b) A beam of light of wavelength 589 nm is directed at the double-slit to produce an interference pattern on a screen placed 120 cm from the slits.The distance between 20 bright fringes is 4.8 mm.Calculate the separation between the slits.

i) In Young's double slit experiment, interference patterns are observed when the two slits are close enough together that the diffracted waves from each slit overlap and interfere with each other. When the slits are too far apart, such as 5.0 cm in this case, the diffracted waves do not overlap sufficiently to create a noticeable interference pattern. The resulting pattern on the screen will simply be two separated bright spots corresponding to each slit.

ii) It is better for the student to observe the interference patterns at a greater distance, around 1.0 m from the slits, because the interference pattern becomes more spread out and easier to observe. When the screen is closer to the slits, the interference pattern appears closer together and may be difficult to distinguish. However, when the screen is farther away, the individual bright and dark fringes become more distinct and easier to observe.

b) To calculate the separation between the slits, we can use the formula:

Δy = (λL) / d

where:
Δy is the distance between the bright fringes (in this case, 4.8 mm),
λ is the wavelength of light (589 nm or 589 × 10^-9 m),
L is the distance from the slits to the screen (120 cm or 1.2 m), and
d is the separation between the slits (what we are trying to find).

Plugging in the values, we have:

4.8 × 10^-3 m = (589 × 10^-9 m) × (1.2 m) / d

To isolate d, we can rearrange the equation:

d = (589 × 10^-9 m) × (1.2 m) / (4.8 × 10^-3 m)

Calculating this, we find:

d ≈ 0.147 × 10^-3 m

Therefore, the separation between the slits is approximately 0.147 mm.