$A$ concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let $O$ be the pole of the mirror and $C$ its centre of curvature. $A$ point object is placed at $C$. It has a real image,also located at $C$. If the mirror is now filled with water,the image will be

Which of the following form$(s)$ a virtual and erect image for all positions of the object?

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l > 0$ from one of the corners as shown in the figure. $A$ ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.
Which of the following statement(s) is(are) correct?
$(A)$ The ray of light will come out for $\theta=30^{\circ}$, for $0 < l < L$.
$(B)$ There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
$(C)$ The ray of light will $NEVER$ come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
$(D)$ The ray of light will come out for $\theta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.

$A$ satisfactory photographic print is obtained when the exposure time is $10 \, s$ at a distance of $2 \, m$ from a $60 \, cd$ lamp. The time of exposure required for the same quality print at a distance of $4 \, m$ from a $120 \, cd$ lamp is $... \, s$.

Which of the following is correct regarding microscope and telescope?

An optical bench has a $1.5 m$ long scale having four equal divisions in each $cm$. While measuring the focal length of a convex lens,the lens is kept at the $75 cm$ mark of the scale and the object pin is kept at the $45 cm$ mark. The image of the object pin on the other side of the lens overlaps with the image pin that is kept at the $135 cm$ mark. In this experiment,the percentage error in the measurement of the focal length of the lens is. . . . .