At most, how many bright fringes can be formed on one side of the central bright fringe (not counting the central bright fringe) when light of $625 \mathrm {~nm}$ falls on a pair of slits that are $6.77 \times 10 ^ { - 6 } \mathrm {~m}$ apart?
A) 9
B) 8
C) 12
D) 11
E) 10

Question

Quizplus · Accepted Answer

The number of bright fringes on one side of the central bright fringe can be calculated using the formula for the angular position of the m-th bright fringe in a double-slit experiment, $\theta_m = m\lambda/d$, where $\lambda$ is the wavelength of the light, $d$ is the distance between the slits, and $m$ is the order number of the fringe. The maximum value of $m$ (which gives the number of bright fringes on one side of the central maximum) is determined by the condition that $\sin(\theta_m) \leq 1$, since the sine of an angle cannot exceed 1. Rearranging the formula gives $m = d/\lambda$. Substituting the given values, $d = 6.77 \times 10^{-6} \mathrm{m}$ and $\lambda = 625 \times 10^{-9} \mathrm{m}$, we get $m = (6.77 \times 10^{-6} \mathrm{m}) / (625 \times 10^{-9} \mathrm{m}) = 10.832$. Since $m$ must be an integer, the maximum number of bright fringes on one side of the central bright fringe is 10.

At Most, How Many Bright Fringes Can Be Formed on One