Two slits $S_1$ and $S_2$ illuminated by a white light source give a white central maxima. A transparent sheet of refractive index 1.25 and thickness $t_1$ is placed in front of $S_1$. Another transparent sheet of refractive index 1.50 and thickness $t_2$ is placed in front of $S_2$. If central maxima is not effected, then ratio of the thickness of the two sheets will be
Answer & explanation
Correct answer: option 2
Since there is no shift in central maxima. Therefore path difference introduced by the two sheets are equal i.e. $(m_1-1)t_1=(m_2-1)t_2$
where 1 m and 2 m are refraction index
$i.e.\,\,\frac{t_1}{t_2}=\frac{(m_2-1)}{(m_1-1)}=\frac{(1.5-1)}{(1.25-1)}=\frac{0.5}{0.25}=2$