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In Young's double slit experiment, a student observes 8 fringes in a certain segment of the screen when a monochromatic light of $\mathrm{600nm}$ wavelength is used. If the wavelength of light is changed to $\mathrm{400nm}$ , then the number of fringes he would observe in the same region of the screen is :
Option: 1
$8$

Option: 2
$9$

Option: 3
$12$

Option: 4
$6$

Answers (1)

best_answer

Let the length of segment be y

Since there are 8 fringes in that segment

$\mathrm{\therefore \quad 8 \beta_{1}=y} \\$ ....(1)

$\mathrm{\beta_{1}=\frac{\lambda_{1} D}{d}=}$ fringe width for wavelength $\mathrm{(\lambda_{1}=600nm)}$

Let say there are $\mathrm{n_{2}}$ fringes of wavelength $\mathrm{\lambda_{2}=400nm}$ in segment $\mathrm{y}$

$\mathrm{\therefore n_{2} \beta_{2}=y}$ ......(2)

From eqn (1)

$\mathrm{8 \beta_{1}=n_{2} \beta_{2}} \\$

$\mathrm{8 \times \lambda_{1}=n_{2} \lambda_{2}} \\$

$\mathrm{8 \times 600=n_{2}(400)} \\$

$\mathrm{n_{2}=12}$

hence correct option is 3

Posted by

Rishabh

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