In Young's double slit experiment,the wavelen | vedclass

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(B) The condition for the $n^{th}$ bright fringe of red light to coincide with the $(n+1)^{th}$ bright fringe of blue light is given by the equality o

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$2$

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(B) The condition for the $n^{th}$ bright fringe of red light to coincide with the $(n+1)^{th}$ bright fringe of blue light is given by the equality of their positions from the central maximum.$y_n(R) = y_{n+1}(B)$Since the position of the $n^{th}$ bright fringe is $y_n = n \lambda \frac{D}{d}$,we have:$n \lambda_R \frac{D}{d} = (n+1) \lambda_B \frac{D}{d}$$n \lambda_R = (n+1) \lambda_B$Substituting the given values:$n 	imes 7800 \, \mathring{A} = (n+1) 	imes 5200 \, \mathring{A}$Dividing both sides by $2600 \, \mathring{A}$:$3n = 2(n+1)$$3n = 2n + 2$$n = 2$Thus,the $2^{nd}$ bright band of red light coincides with the $3^{rd}$ bright band of blue light.

In Young's double slit experiment,the wavelength of red light is $7800 \, \mathring{A}$ and that of blue light is $5200 \, \mathring{A}$. The value of $n$ for which the $n^{th}$ bright band due to red light coincides with the $(n + 1)^{th}$ bright band due to blue light is:

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