Question

In young's double slit experiment, the width of the fringes obtained with light of wavelength $6000 \mathring{A}$ is $2 mm$. What will be the fringe width, if the entire apparatus is immersed in a liquid of refractive index $1.33 ?$

• A. $5 mm$
• B. $3 mm$
• C. $1.5 mm$
• D. $1 mm$

Answer 1

Answer: (C)

$\beta=\frac{\lambda D }{ d }, \beta^{\prime}=\frac{\lambda^{\prime} D }{ d }$
$\therefore \frac{\beta^{\prime}}{\beta}=\frac{\lambda^{\prime} D}{d} \times \frac{d}{\lambda D}=\frac{\lambda^{\prime}}{\lambda}=\frac{1}{\mu}$
$\beta^{\prime}=\frac{\beta}{\mu}=\frac{2}{1.33}=1.5\, mm$