Question

A light of wavelength $6000\mathring{A}$ shines on two narrow slits separated by a distance $1.0mm$ and illuminates a screen at a distance $1.5m$ away. When one slit is covered by a thin glass plate of refractive index $1.8$ and other slit by a thin glass plate of refractive index $\mu$, the central maxima shifts by $0.1rad$. Both plates have the same thickness of $0.5mm$. The value of refractive index $\mu$ of glass is:

• A. $1.4$
• B. $1.5$
• C. $1.6$
• D. none of these

Answer 1

Answer: (C)

$1.6$

Lateral shift $\overline{X}=\frac{D}{d}(\mu -1)t$ and $\tan \theta \approx \theta =\frac{\overline{X}}{D}$

Central maxima shift $\Delta \theta =\frac{t}{d}[(1.8-1)-(\mu -1)]=\frac{t}{d}(1.8-\mu )$

Refractive index of glass $\mu =1.8-\frac{\Delta \theta d}{t}=1.8-\frac{0.1\times 1}{0.5}=1.8-0.2=1.6$