List of top Physics Questions on Refractive index asked in UP Board XII

Which of the following ray diagrams is correct, when \( n_1 \) is the refractive index of the medium and \( n_2 \) is of the lens material (\( n_1>n_2 \))? 
 

Two parallel plate capacitors of capacitances \( C \) and \( 2C \) are joined with a battery of voltage difference \( V \) as shown in the figure. If the battery is removed and the space between the plates of the capacitor of capacitance \( C \) is completely filled with a material of dielectric constant \( K \), then find out:

• i) Total capacitance of the combination
• ii) Final voltage difference across the combination
• iii) Total energy stored in the combination.

Define the coefficient of mutual inductance.
The coefficient of mutual inductance (\(M\)) is a measure of the ability of one coil to induce an electromotive force (EMF) in a nearby coil due to a changing current in the first coil. It is given by: \[ e = -M \frac{di}{dt} \]

If a current \( i = 10 \sin(100 \pi t) \, \mathrm{A} \) is flowing in a primary coil, and the maximum induced electromotive force in the secondary coil placed near it is \( 5 \pi \, \mathrm{volt} \), then the coefficient of mutual induction between these coils needs to be determined.

State the conclusions of Rutherford's \( \alpha \)-particle scattering experiment.