Question

If the source is now changed to green light of wavelength ${10}^{-7}m$ and a new glass plate is placed in place of the previous glass plate, the central fringe shifts to a position initially occupied by the sixth bright fringe due to red light without the glass plate. What is refractive index of new glass plate?

• A. $2.6$ $\mu m$
• B. $1.6$ $\mu m$
• C. $1.2$ $\mu m$
• D. $2.2$ $\mu m$

Answer 1

The correct option is B $1.6$ $\mu m$

Give:

The wavelength of red light, ${\lambda }_R=7\times {10}^{-7}m$

Refractive index of the glass plate, $\mu =1.5$

Central bright fringe shift by ${10}^{-3}m$ to the fifth bright fringe.

The wavelength of green light, ${\lambda }_G={10}^{-7}m$

To find:

Refractive index of the new glass plate

For Red Light

The shifts of fringes due to glass plate =$\frac{Dt(\mu –1)}{d}$,

where $t$ is the thickness of the plate.

This shift is equal to $5\omega$, where $\omega$ is the fringe width

Then,

$\frac{Dt(\mu –1)}{d}=5\omega$

$\Rightarrow \frac{Dt(\mu –1)}{d}=\frac{5{\lambda }_{R}D}{d}$

$t=\frac{5\lambda }{(\mu -1)}=\frac{5\times 7\times {10}^{-7}}{1.5–1}=7\times {10}^{–6}m$

For Green Light : Let ${\mu }^{\prime }$ be the refractive index of glass plate of thickness $t$ for green light.

${\lambda }_g=5\times {10}^{–7}m$

$\frac{Dt({\mu }^{\prime }–1)}{d}=\frac{6{\lambda }_{R}D}{d}$

$\Rightarrow {\mu }^{\prime }=\frac{6{\lambda }_R}{t}+1=\frac{6\times 7\times {10}^{-7}}{7\times {10}^{-6}}+1$

${\mu }^{\prime }=1.6$