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 nm falls on a pair of slits that are $6.77 \times 10 ^ { - 6 } \mathrm {~m}$ apart?
A) 10
B) 9
C) 8
D) 11
E) 12

Question

Quizplus · Accepted Answer

The number of bright fringes on one side of the central bright fringe is given by:$$N = \frac{aW}{\lambda}-1$$where:* N is the number of bright fringes* a is the slit separation* W is the screen width* \lambda is the wavelength of lightIn this problem, we are given:* a = $6.77 \times 10 ^ { - 6 } \mathrm {~m}$* \lambda = 625 nm = $6.25 \times 10 ^ { - 7 } \mathrm {~m}$We do not know the screen width, but we can assume that it is large enough to accommodate all of the bright fringes. Therefore, we can use the following approximation:$$W \approx \frac{aN}{\lambda}$$Substituting this approximation into the equation for N, we get:$$N = \frac{a^2}{\lambda^2}-1$$Plugging in the values for a and \lambda, we get:$$N = \frac{(6.77 \times 10 ^ { - 6 } \mathrm {~m})^2}{(6.25 \times 10 ^ { - 7 } \mathrm {~m})^2}-1 = 10$$Therefore, the correct answer is A) 10.

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