In a Young’s double slit experiment, the \( n^{\mathrm{th}} \) bright fringe for a light of wavelength \( 5000\,\mathring{\mathrm{A}} \) coincides with \( (n+1)^{\mathrm{th}} \) bright fringe for light of wavelength \( 4000\,\mathring{\mathrm{A}} \). The value of n is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4
In Young's double slit experiment the position of the \( n \)th bright fringe is \( y_n = n\lambda D/d \). The two fringes coincide when they are at the same distance from the centre.
\( \displaystyle n\lambda_1 \frac{D}{d} = (n+1)\lambda_2 \frac{D}{d} \;\Rightarrow\; n \times 5000 = (n+1) \times 4000 \)
\( \displaystyle 5n = 4n + 4 \;\Rightarrow\; n = 4 \)