Chapter 33: Q. 3 (page 954)

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. Fringe $C$ 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" $500 nm$ . 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

Expert verified

(a) The wavelength of the light If $λ$ increases, $Δ y$ will decrease.

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

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

(d) $2 λ = 1000 nm$ 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 $Δ y = λ L / d$ .

(a) If $λ$ increases, $Δ y$ will decrease.

(b) If d decreases, $Δ y$ will increase.

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