$A$ 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

$A$ ray of sunlight enters a spherical water droplet $(n = 4/3)$ at an angle of incidence $53^o$ measured with respect to the normal to the surface. It is reflected from the back surface of the droplet and re-enters into air. The angle between the incoming and outgoing ray is $.......^o$ [Take $\sin \,53^o = 0.8$]

If the focal length of the objective lens is increased,then the magnifying power of:

$A$ particle is oscillating on the $X-$ axis with an amplitude $2\, cm$ about the point $x_0 = 10\, cm$ with a frequency $\omega $. $A$ concave mirror of focal length $5\, cm$ is placed at the origin (see figure). Identify the correct statements.
$(A)$ The image executes periodic motion
$(B)$ The image executes non-periodic motion
$(C)$ The turning points of the image are asymmetric w.r.t the image of the point at $x = 10\, cm$
$(D)$ The distance between the turning points of the oscillation of the image is $\frac{100}{21}\, cm$

$A$ concave mirror of radius of curvature $h$ is placed at the bottom of a tank containing a liquid of refractive index $\mu$ up to a depth $d$. An object $P$ is placed at a height $h$ above the bottom of the mirror. Outside the liquid,an observer $O$ views the object and its image in the mirror. The apparent distance between these two will be

Five lumen/watt is the luminous efficiency of a lamp and its luminous intensity is $35$ candela. The power of the lamp is.......$W$