Question

In Young's double slit experiment, fringes are obtained using light of wavelength $4800 \, \mathring{A}$ One slit is covered with a thin glass film of refractive index $1.4$ and another slit is covered by a film of same thickness but refractive index $1.7 .$ By doing so, the central fringe is shifted to fifth bright fringe in the original pattern. The thickness of glass film is

• A. $2 \times 10^{-3} mm$
• B. $4 \times 10^{-3} mm$
• C. $6 \times 10^{-3} mm$
• D. $8 \times 10^{-3} mm$

Answer 1

Answer: (D)

As per question,
$\left(\mu_{1}-1\right) t \frac{D}{d}-\left(\mu_{2}-1\right) \frac{t D}{d}=\frac{5 \lambda D}{d}$
${[(1.7-1)-(1.4-1)] \frac{t D}{d}=\frac{5 \lambda D}{d}}$
$\therefore t=\frac{5 \lambda}{0.3}=\frac{5 \times 4800 \times 10^{-10}}{0.3}$
$=8 \times 10^{-6} m =8 \times 10^{-3} \,mm$