Question

Two sources of light of wavelength $2500\, ? $ and $3500 \,? $ are used in Young?? double slit experiment simultaneously. Which orders of fringes of two wavelength patterns coincide?

• A. $3^{rd}$ order of $1^{st}$ source and $5^{th}$ of the $2^{nd}$
• B. $7^{th}$ order of $1^{st}$ and $5^{th}$ order of $2^{nd}$
• C. $5^{th}$ order of $1^{st}$ and $3^{rd}$ order of $2^{nd}$
• D. $5^{th}$ order of $1^{st}$ and $7^{th}$ order of $2^{nd}$

Answer 1

The Correct Option is B

Let $n^{th}$ fringe of $2500 ?$ coincide with $\left(n - 2 \right) ^{th}$ fringe of $3500 ?$. $\therefore 3500\left(n-2\right) = 2500 \times n $ $ 1000 n = 7000$, or $ n = 7 $ $ \therefore 7^{th}$ order fringe of $1^{st }$ source will coincide with $5^{th}$ order fringe of $2^{nd}$ source,