$A$ small lamp is hung at a height of $8 \text{ feet}$ above the centre of a round table of diameter $16 \text{ feet}$. The ratio of intensities of illumination at the centre and at points on the circumference of the table will be

Which of the following statements is correct?

When seen in green light,the saffron and green portions of our National Flag will appear to be

$A$ beaker of radius $r$ is filled with water (refractive index $\frac{4}{3}$) up to a height $H$ as shown in the figure. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This makes the water surface curved so that the difference in the height of the water level at the center and at the circumference of the beaker is $h$ $(h \ll H, h \ll r)$,as shown in the figure. Take this surface to be approximately spherical with a radius of curvature $R$. Which of the following is/are correct? ($g$ is the acceleration due to gravity)
$(A)$ $R=\frac{h^2+r^2}{2 h}$
$(B)$ $R=\frac{r^2}{2 h}$
$(C)$ Apparent depth of the bottom of the beaker is close to $\frac{3 H}{4}\left(1+\frac{\omega^2 H}{4 g}\right)^{-1}$
$(D)$ Apparent depth of the bottom of the beaker is close to $\frac{3 H}{2}\left(1+\frac{\omega^2 H}{2 g}\right)^{-1}$

In the figure shown,consider the first reflection at the plane mirror and the second at the convex mirror. $AB$ is the object.

$A$ photograph of the moon was taken with a telescope. Later on, it was found that a housefly was sitting on the objective lens of the telescope. In the photograph: