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 $\_\_\_\_$ .

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A . The magnetic energy stored inside the cube is $\alpha \times 10^{-14} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

$$ \left(\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}, \pi=3.14\right) $$