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(D) The condition for the $n^{th}$ bright fringe is $y_n = n \frac{D \lambda_1}{d}$. For $n = 4$ and $\lambda_1 = 6300 \, \mathring{A}$,$y_4 = 4 \frac

Vedclass · Accepted Answer

$5600$

Vedclass · Answer

(D) The condition for the $n^{th}$ bright fringe is $y_n = n \frac{D \lambda_1}{d}$. For $n = 4$ and $\lambda_1 = 6300 \, \mathring{A}$,$y_4 = 4 \frac{D 	imes 6300}{d}$.The condition for the $m^{th}$ dark fringe is $y_m = (m - \frac{1}{2}) \frac{D \lambda_2}{d}$. For $m = 5$ and $\lambda_2 = \lambda$,$y_5 = (5 - 0.5) \frac{D \lambda}{d} = 4.5 \frac{D \lambda}{d} = \frac{9}{2} \frac{D \lambda}{d}$.Since the fringes coincide,$y_4 = y_5$:$4 \frac{D 	imes 6300}{d} = \frac{9}{2} \frac{D \lambda}{d}$.Canceling $\frac{D}{d}$ from both sides:$4 	imes 6300 = 4.5 	imes \lambda$.$\lambda = \frac{4 	imes 6300}{4.5} = \frac{25200}{4.5} = 5600 \, \mathring{A}$.

Similar Questions

In a Young's double-slit experiment,light of wavelength $5890 \ \mathring A$ is used,and the angular fringe width on the screen is $0.20^\circ$. If the entire apparatus is immersed in water,find the new angular fringe width. (Refractive index of water $\mu = 4/3$) (in $^\circ$)

If the monochromatic source in Young's double slit experiment is replaced by white light,then

In Young's double-slit experiment,using light of wavelength $\lambda = 5890 \ \mathring{A}$,the angular width of the fringe is $0.20^\circ$. To increase the angular width by $10\%$,the wavelength must be increased by .......... $\mathring{A}$.

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