You set two slits 30 mm apart and 50 cm from a screen.When you illuminate the slits with light of wavelength 600 nm,the distance between the second and third dark interference lines is
A)1.0 mm
B)2.0 mm
C)3.0 mm
D)0.30 mm
E)6.0 mm

Question

Quizplus · Accepted Answer

The distance between dark fringes in a double-slit interference pattern can be calculated using the formula $y_m = \frac{(m + 1/2) \lambda L}{d}$, where $y_m$ is the distance from the central maximum to the $m$th dark fringe, $\lambda$ is the wavelength of the light, $L$ is the distance from the slits to the screen, $d$ is the distance between the slits, and $m$ is the order number of the dark fringe. For the second and third dark lines, we calculate the positions of the $m = 1$ and $m = 2$ dark fringes and subtract the former from the latter to find the distance between them.For $m = 1$: $y_1 = \frac{(1 + 1/2) \lambda L}{d} = \frac{3/2 \times 600 \times 10^{-9} \times 0.5}{30 \times 10^{-3}} = 1.5 \times 10^{-2}$ m = 1.5 mmFor $m = 2$: $y_2 = \frac{(2 + 1/2) \lambda L}{d} = \frac{5/2 \times 600 \times 10^{-9} \times 0.5}{30 \times 10^{-3}} = 2.5 \times 10^{-2}$ m = 2.5 mmThe distance between the second and third dark lines is $2.5 mm - 1.5 mm = 1.0 mm$, which seems to contradict the initial selection. However, the correct approach to find the distance between the second and third dark fringes involves understanding the pattern's geometry and using the correct formula. Given the discrepancy in the explanation, let's correct the understanding:The correct formula to use for the distance between dark fringes (or bright fringes) in a double-slit experiment is actually $y = \frac{m\lambda L}{d}$, where $m$ is an integer (for bright fringes) or half-integer (for dark fringes). The difference in position between two adjacent fringes (dark or bright) can be found by calculating the position of one fringe and then subtracting the position of the previous fringe.Given the mistake in the initial explanation, the correct calculation directly for the distance between the second and third dark lines should consider the formula for fringe separation, which is $\Delta y = \frac{\lambda L}{d}$. This gives us $\Delta y = \frac{600 \times 10^{-9} \times 0.5}{30 \times 10^{-3}} = 1.0 \times 10^{-2}$ m = 1.0 mm, which matches option A, not B as initially stated. The correct explanation involves recognizing the error in the calculation process and correctly applying the formula for fringe separation in a double-slit experiment.

You Set Two Slits 30 Mm Apart and 50 Cm