Monochromatic light of wavelength 400 nm and 560 nm are incident simultaneously and normally on a double slits apparatus whose slit separation is 0.1 mm and screen distance is 1 m. Distance between areas of total darkness will be [20

Question

Monochromatic light of wavelength 400 nm and 560 nm are incident simultaneously and normally on a double slits apparatus whose slit separation is 0.1 mm and screen distance is 1 m. Distance between areas of total darkness will be [2004]

Smart Achievers · Accepted Answer

(4)

At the area of total darkness, minima will occur for both the wavelengths incident simultaneously and normally.

$∴$ $\frac{(2 n + 1)}{2} λ_{1} = \frac{(2 m + 1)}{2} λ_{2}$ $\Rightarrow (2 n + 1) λ_{1} = (2 m + 1) λ_{2}$

or, $\frac{(2 n + 1)}{(2 m + 1)} = \frac{560}{400} = \frac{7}{5}$ or $10 n = 14 m + 2$

By inspection, for $m = 2, n = 3$ and for $m = 7, n = 10$ , the distance between them will be the distance between such points.

i.e., $Δ s = \frac{D λ_{1}}{d} [\frac{(2 n_{2} + 1) - (2 n_{1} + 1)}{2}]$

Put $n_{2} = 10, n_{1} = 3$

$Δ s = \frac{1 \times (400 \times 10^{- 9})}{0.1 \times 10^{- 3}} [\frac{21 - 7}{2}] = 28 mm$

Solution

Q.
Monochromatic light of wavelength 400 nm and 560 nm are incident simultaneously and normally on a double slits apparatus whose slit separation is 0.1 mm and screen distance is 1 m. Distance between areas of total darkness will be [2004]

1 4 mm

2 5.6 mm

3 14 mm

4 28 mm

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