$A$ 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 $\sin \,53^o = 0.8$]

$A$ 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 $\frac{100}{21}\, cm$

Which of the following is correct regarding microscope and telescope?

Ray optics is valid when characteristic dimensions are:

$A$ ray of light falls on the surface of a spherical glass paperweight,making an angle $\alpha$ with the normal,and is refracted in the medium at an angle $\beta$. What is the angle of deviation of the emergent ray from the direction of the incident ray?

An electric lamp is fixed at the ceiling of a circular tunnel as shown in the figure. What is the ratio of the intensities of light at base $A$ and a point $B$ on the wall?