In a double slit experiment with monochromatic light, fringes are… - Vidyadip

MCQ

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5 \times 10^{-2} \,m$ towards the slits, the change in fringe width is $3 \times 10^{-3} \,cm$. If the distance between the slits is $1 \,mm$, then the wavelength of the light will be_______ $nm$

A
$500$
✓
$600$
C
$700$
D
$900$

✓

Answer

Correct option: B.

$600$

b
$\beta=\frac{\lambda D}{d}$
$\Delta \beta=\frac{\lambda}{ d } \Delta D$
$\lambda=\frac{\Delta \beta \cdot d}{\Delta D }$
$=\frac{3 \times 10^{-5} \times 1 \times 10^{-3}}{5 \times 10^{-2}}$
$=60 \times 10^{-8}=600 \times 10^{-9} \,m$
$=600 \,nm$

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