In a YDSE, slits are 0.5 text mm apart and the screen is 150 text cm away. Using wavelengths 650 text nm and 520 text nm , find the minimum distance from the central maximum where bright fringes from both wavelengths overlap.

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EEJ MAIN Physics QUESTION #7048

Question 1

In a YDSE, slits are $0.5 \text{ mm}$ apart and the screen is $150 \text{ cm}$ away. Using wavelengths $650 \text{ nm}$ and $520 \text{ nm}$, find the minimum distance from the central maximum where bright fringes from both wavelengths overlap.

$15.6 \text{ mm}$
$1.56 \text{ mm}$
$7.8 \text{ mm}$✔️
$9.75 \text{ mm}$

Correct Answer Explanation

Overlap occurs when $n_1 \lambda_1 = n_2 \lambda_2$.

$n_1(650) = n_2(520) \implies \frac{n_1}{n_2} = \frac{520}{650} = \frac{4}{5}$.

Distance $y = \frac{n_1 \lambda_1 D}{d} = \frac{4 \times 650 \times 10^{-9} \times 1.5}{0.5 \times 10^{-3}} = 7.8 \times 10^{-3} \text{ m} = 7.8 \text{ mm}$.

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