Rays from the Sun converge at a point $15 \, cm$ in front of a concave mirror. Where should an object be placed so that the size of its image is equal to the size of the object?

Where should an object be placed to use a convex lens as a simple microscope?

Which of the following can produce a magnification of $+5$ as well as $-5$?

If an object is placed between two plane mirrors inclined at an angle of $45^{\circ}$,then the number of images formed will be $9$. State whether this statement is True or False.

$A$ ray of light enters from a medium with refractive index $n_1$ into a medium with refractive index $n_2$. If the angle of incidence is $\theta_1$ and the angle of refraction is $\theta_2$,then $\sin \theta_1 / \sin \theta_2 = \dots$

One half of a convex lens is covered with a black paper.
$(a)$ Show the formation of the image of an object placed at $2F_{1}$ of such a covered lens with the help of a ray diagram. Mention the position and nature of the image.
$(b)$ Draw the ray diagram for the same object at the same position in front of the same lens,but now uncovered. Will there be any difference in the image obtained in the two cases? Give a reason for your answer.