A tabletop two-slit interference experiment consists of a laser pointer shining through two narrow, closely spaced slits in an opaque barrier. The light from the slits produces a characteristic pattern of alternating bright and dark regions on a nearby wall. Listed are five ways to modify the parameters of the experiment. Match each modification according to the effect it would have on the spacing between the bright spots on the wall. In each case, assume that everything else is held constant. a. Causes the spacing between the bright spots on the wall to increase.
b. Causes the spacing between the bright spots on the wall to decrease.
c. Has effed on the spacing between the bright spots on the wall.

1. increasing the distance d between the two slits in the barrier
2. increasing the brightness of the laser light
3. increasing the distance L from the slits to the wall
4. increasing the distance x from the laser to the slits
5. increasing the wavelength of the laser light

a - 3, 5

b - 1

c - 2, 4

Explanation:

a). The distance between fringes on the screen

where, λ is wavelength, m is order of pattern, L is distance between slit and screen, d is separation between slits.

Now we analyze that spacing between bright spots increases as increasing distance L from slits to wall and increasing the wavelength of the laser light, λ.

b). The spacing between the bright spots decreases as the distance between the two slits increases.

c). Has no effect on the spacing between the bright spots on the wall by increasing the distance from the laser to the slits as well as increasing the brightness of the laser.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.