A thin half ring of radius 35 cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100 \mathrm{~V} / \mathrm{m}$, then the value of $Q$ is $\_\_\_\_$ nC .

$$ \left(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2 \text { and } \pi=3.14\right) $$

The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage of 5 V as shown in the figure below. The current through resistance $R_S$ is 0.5 mA .

The minimum value of the resistance of $R_S$, to ensure that the LED is not damaged is $\_\_\_\_$ $\mathrm{k} \Omega$.

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L \mathrm{~m}$, measures the intensity as $I_{\mathrm{o}}$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45^{\circ}$. The measured intensity at new location will be $\_\_\_\_$ .

A spherical interface lens of radius $R$ separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of $4 R$ in front of spherical interface. The magnitude of the magnification of point source image is $\_\_\_\_$ .