$A$ laser light of wavelength $630 \, nm$ is incident on a pair of slits,and the fringe width of the interference pattern produced is $8.1 \, mm$. In another interference pattern produced by a different light,the fringe width is $7.2 \, mm$. Find the wavelength of this second light in $nm$.

If the Young's double slit experiment is performed with white light,then which of the following is not true?

In a Young's double slit experiment,the fringe width will remain the same if ($D =$ distance between screen and plane of slits,$d =$ separation between two slits,and $\lambda =$ wavelength of light used).

In Young's double-slit experiment,if the distance between the slits is twice the wavelength,the number of possible interference maxima is:

$A$ light source,which emits two wavelengths $\lambda_1=400 \ nm$ and $\lambda_2=600 \ nm$,is used in a Young's double slit experiment. If recorded fringe widths for $\lambda_1$ and $\lambda_2$ are $\beta_1$ and $\beta_2$ and the number of fringes for them within a distance $y$ on one side of the central maximum are $m_1$ and $m_2$,respectively,then
$(A)$ $\beta_2 > \beta_1$
$(B)$ $m_1 > m_2$
$(C)$ From the central maximum,$3^{\text{rd}}$ maximum of $\lambda_2$ overlaps with $5^{\text{th}}$ minimum of $\lambda_1$
$(D)$ The angular separation of fringes for $\lambda_1$ is greater than $\lambda_2$

In a Young's double slit experiment,light of $500 \ nm$ is used to produce an interference pattern. When the distance between the slits is $0.05 \ mm$,the angular width (in degrees) of the fringes formed on the distant screen is close to $........^o$.