Question

In Young's double-slit experiment, the y-coordinates of central maxima and 10th maxima are $2cm$ and $5cm$, respectively. When the YDSE apparatus is immersed in a liquid of refractive index $1.5$, the corresponding y-coordinates will be

• A. $2cm$, $7.5cm$
• B. $3cm$, $6cm$
• C. $2cm$, $4cm$
• D. $4/3cm$, $10/3cm$

Answer 1

The correct option is C $2cm$, $4cm$

For YDSE appratus in air:

For central maxima ($n=0$)

$y_{0}d/D-d\sin \theta =0$

$\sin \theta =y/D=2/D$ (given $y_0=2$)

For ${10}^{th}$ maxima ($n=10$)

$y_{10}d/D-d\sin \theta =10\lambda$

$5d/D-d\sin \theta =10\lambda$ (given $y_{10}=5$)

Putting the value of $\sin \theta$ in this equation, we get

$\lambda =\frac{3d}{10D}$

For YDSE appratus in liquid of refractive index, $n=1.5$

For central maxima ($n=0$)

$y_0^{\prime }d/D-d\sin \theta =0$

As the y coordinate of central maximum doesn't depend upon wavelength, therefore it will remain same as in air, $y_0^{\prime }=y_0=2cm$

For ${10}^{th}$ maxima ($n=10$)

$y_{10}^{\prime }d/D-d\sin \theta =10\lambda /1.5$

$y_{10}^{\prime }d/D-d\sin \theta =10/1.5\times 3d/10$

Putting the value of $\sin \theta$ in this equation, we get

$y_{10}^{\prime }=4cm$