Question

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. Fringe$\mathrm{C}$is the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" $500\mathrm{nm}$. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

Short answer

(a) The wavelength of the light If $\lambda$increases, $\Delta y$will decrease.

(b) The spacing between the If d decreases, $\Delta y$will increase.

(c)The distance to the screen If L decreases, $\Delta y$will decrease.

(d) $2\lambda =1000\mathrm{nm}$farther from the dot on the screen

Step-by-step solution

definition of fringe spacing

Fringe spacing is the distance between any two consecutive bright or dark fringes. The spacing and thickness of a dark and a bright fringe are the same.

Find fringe spacing

We know that $\mathrm{\Delta }y=\lambda L/d$.

(a) If$\lambda$ increases, $\mathrm{\Delta }y$will decrease.

(b) If d decreases, $\mathrm{\Delta }y$will increase.

(c) If L decreases, $\mathrm{\Delta }y$will decrease.

(d) Since the dot is in the $m=2$bright fringe and each bright fringe is $\lambda$distance apart, hence, the path length difference from the two slits is$2\lambda =1000nm$ .