please help solve 3 3. The figure shows the viewing screen in a double-slit expe

Question

please help solve 3

3. The figure shows the viewing screen in a double-slit experiment. Fringe C is the central maximum. For (a)-(c) say whether the fringe spacing will increase, decrease or stay the same if the described change is made. Give an explanation for each. AB DE a. The distance to the screen is increased. b. The spacing between the slits is increased. c. The wavelength of the light is increased. d. Suppose the wavelength of the light is 500 nm. How much farther is it from the dot in the center of fringe E to the more distant slit than it is from the dot to the nearest slit?

Explanation / Answer

fringe spacing,

y = D / d ----------------------->eqn[1]

where

= wavelength

D = distance between screen and slits

d = separation of the slits

part a)

from eqn[1],

Fringe spacing is directly proportional to the distance of the screen

given, the distance of the screen is increased,

hence, the fringe spacing y also increase

Part b)

from eqn[1],

fringe spacing is inversely proportional to tje spacing between the slits.

given, spacing between the slits is increased,

hence, fringe spacing y decreases.

Part c)

from eqn[1],

y

Fringe spacing is directly proportional to the wavelength

given, wavelength of light is increased,

hence, fringe spacing y also increases.

Part d)

As C is the given central maximum.

Hence, E is the 2nd bright fringe.

Therefore, the path difference from the left slit to the right slit on the dot is say r.

For the constructive interference,

path difference r = m

Where, m is the order of the fringe and we know E is the 2nd order.

therefore, r = 2

given, = 500nm

therefore, r = 2*500

r = 1000 nm

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