$A$ concave mirror has a radius of curvature of $40\, cm$. It is at the bottom of a glass that has water filled up to $5\, cm$ (see figure). If a small particle is floating on the surface of water,its image as seen from directly above the glass is at a distance $d$ from the surface of water. The value of $d$ is close to ......$cm$ (Refractive index of water $= 1.33$)

$A$ $60 \text{ W}$ bulb is hung over the center of a table of size $4 \text{ m} \times 4 \text{ m}$ at a height of $3 \text{ m}$. The ratio of the intensities of illumination at a point on the center of the edge $(A)$ and at the corner of the table $(B)$ is:

The mirrors are perpendicular to each other as shown in the figure. $A$ light ray $AB$ is incident on the mirror $M_1$. The reflected ray then undergoes a reflection from the mirror $M_2$. The final ray after reflection from $M_2$ will be parallel to the incident ray, if

$A$ light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_0$. The ray partially refracts into the sphere with angle of refraction $\phi_0$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

$List-I$	$List-II$
$(P)$ If $n=2$ and $\alpha=180^{\circ}$,then all the possible values of $\theta_0$ will be	$(1)$ $30^{\circ}$ and $0^{\circ}$
$(Q)$ If $n=\sqrt{3}$ and $\alpha=180^{\circ}$,then all the possible values of $\theta_0$ will be	$(2)$ $60^{\circ}$ and $0^{\circ}$
$(R)$ If $n=\sqrt{3}$ and $\alpha=180^{\circ}$,then all the possible values of $\phi_0$ will be	$(3)$ $45^{\circ}$ and $0^{\circ}$
$(S)$ If $n=\sqrt{2}$ and $\theta_0=45^{\circ}$,then all the possible values of $\alpha$ will be	$(4)$ $150^{\circ}$
	$(5)$ $0^{\circ}$

$A$ 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

For a candle of $40$ power,the exposure time required for a photographic print at a distance of $0.6 \, m$ is $20 \, s$. What will be the exposure time required for the same print at a distance of $1.2 \, m$ using a candle of $20$ power?