Physics M.C.Q (1 Marks)

1. Radiation pressure is I/c if the wave is totally absorbed.

3. Radiation pressure is 2I/c if the wave is totally reflected.
4. Radiation pressure is in the range I/c < p < 2I/c for real surfaces.

1. Radiation force/pressure supports photon theory of radiation.
2. If radiation falls abliquely, then appropriate projection of area vector is taken.

3. $\frac{\text{k}}{\omega}$

2. $\frac{1}{\sqrt\mu\epsilon}$

1. Increases.
2. Decreases.

4. None of the above is correct

1. $\hat{\text{k}}\text{ and }\hat{\text{j}}$

1. AC only

2. 2.2A

4. Double the frequency of the wave.

Givne energy flux $\phi=20\frac{\text{W}}{\text{cm}^2}$
Area, $A = 30\ cm^2$
Time, $t = 30min = 30 \times 60s$
Now, total energy falling on the surface in time $t$ is,
$\text{U}=\phi\text{At}=20\times30\times(30\times60)\text{J}$
Momentum of the incident light $=\frac{\text{U}}{\text{c}}$
$=\frac{20\times30\times(30\times60)}{3\times10^{8}}=36\times10^{-4}\text{kg-ms}^{-1}$
Momentum of the reflected light $= 0$
$\therefore$ Momentum delivered to the surface
$=36\times10^{-4}-0=36\times10^{-4}\text{kg-ms}^{-1}$
Important points
Mass of photon:
Actually rest mass of the photon is zero. But its effective mass is given as $\text{E}=\text{mc}^2=\text{hv}$
$\Rightarrow\ \text{m}=\frac{\text{E}}{\text{C}^2}=\frac{\text{hv}}{\text{C}^2}=\frac{\text{h}}{\text{c}\lambda}$. Thsi mass is also known as kintic mass of the photon.
Momentum of the photon:
Momentum $\text{p}=\text{m}\times\text{c}=\frac{\text{E}}{\text{c}}=\frac{\text{hv}}{\text{c}}=\frac{\text{h}}{\lambda}$
Number of emitted photons:
The number of photons emitted per second from a source of monochromatic radiation of wavelengh $\lambda$ and power $P$ is given as $\text{(n)}=\frac{\text{P}}{\text{E}}=\frac{\text{P}}{\text{hv}}=\frac{\text{P}\lambda}{\text{hc}}$; where $E =$ energy of each photon
Inrensity of light $(I):$
Energy crossing per unit area normally per second is called intensity or energy flux
i.e. $\text{I}=\frac{\text{E}}{\text{At}}=\frac{\text{P}}{\text{A}}\Big(\frac{\text{E}}{\text{t}}=\text{P}=\text{radiation Power}\Big)$
At a distance r from a point source of power $P$ intensity is given by $\text{I}=\frac{\text{P}}{4\pi\text{r}^2}\Rightarrow\ \text{I}\propto\frac{1}{\text{r}^2}$.

3. $\frac{\text{L}^2}{\text{T}^2}$

2. $\pi$

3. increases or decreases

4. Both of them.

3. 7.5m

2. $\text{E}_\text{r}=\text{E}_0\hat{\text{i}}\cos(\text{kz}+\omega\text{t})$

2. ​​​​$\frac{\pi}{2}$

2. perpendicular to the electric field $\overrightarrow{\text{S}}$

1. The associated magnetic field is given as $\text{B}=\frac{1}{\text{c}}\big(\text{E}_1\hat{\text{i}}+\text{E}_2\hat{\text{j}}\big)\cos(\text{kz}-\omega\text{t})$.

4. ​​​​​​​The given electromagnetic wave is plane polarised.

4. 60°

1. $\frac{0.166\times10^{-8}\text{N}}{\text{m}^2}$

4. $\sqrt{2}\text{E}.$

3. Mutually perpendicular directions and are in phase

1. $2\mathring{\text{A}}$

2. Halved

3. $\text{p}\neq0,\text{ E}\neq0$

4. Both (b) and (©)

1. The associated magnetic field is given as $\text{B}=\frac{1}{\text{c}}\text{k}\times\text{E}=\frac{1}{\omega}(\hat{\text{k}}\times\text{E})$.
2. The electromagnetic field can be written in terms of the associated magnetic field as $\text{E}=\text{c}(\text{B}\times\hat{\text{k}})$.
3. $\hat{\text{k}}.\text{E}=0,\hat{\text{k}}.\text{B}=0.$

1. The direction of propagation of an eletromagnetic wave is always along the direction of vector product $\vec{\text{E}}\times\vec{\text{B}}$. Refer to Figure.

2. $\vec{\text{E}}=\text{E}\hat{\text{i}}=\text{cB}(\hat{\text{j}}\times\hat{\text{k}})=\text{c}(\text{B}\hat{\text{j}}\times\text{k})=\text{c}(\vec{\text{B}}\times\hat{\text{k}})$
3. $\hat{\text{k}}.\vec{\text{E}}=\hat{\text{k}}.(\text{E}\hat{\text{i}})=0,\vec{\text{k}}.\vec{\text{B}}=\vec{\text{k}}.(\text{B}\hat{\text{j}})=0$
4. $\hat{\text{k}}\times\vec{\text{E}}=\hat{\text{k}}\times(\text{E}\hat{\text{i}})=\text{E}(\hat{\text{k}}\times\hat{\text{i}})=\text{E}\hat{\text{j}}$ and $\hat{\text{k}}\times\vec{\text{B}}=\hat{\text{k}}\times(\text{B}\hat{\text{j}})=\text{B}(\hat{\text{k}}\times\hat{\text{j}})=-\text{B}\hat{\text{i}}$.

2. $\lambda_1$ and $\lambda_2$ are variable

1. $\text{E}_0\text{k}=\text{B}_0\omega$

3. $\overrightarrow{\text{E}}\times\overrightarrow{\text{B}}$

2. Reciprocal of speed of light in vacuum

1. Towards +X direction

4. $\overrightarrow{\text{E}}\times\overrightarrow{\text{B}}$

2. $\frac{\pi}{2}$

4. Deflects and gradually comes to the original position in a time that is large compared to the time constant.

4. E × B.

3. $0.025\mu\text{s}$

2. Is dependent on nature of surface and intensity of light used

3. For all intensities.

4. For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{\text{E}}=\frac{1}{\sqrt{2}}\text{E}_\text{yz}(\text{x,t})(\hat{\text{y}}-\hat{\text{z}})$ and the magnetic field is $\overrightarrow{\text{B}}=\frac{1}{\sqrt{2}}\text{E}_\text{yz}(\text{x,t})(\hat{\text{y}}+\hat{\text{z}})$

1. Electric field.
2. Magnetic field.

2. $\frac{2000\text{Volt}}{\text{meter}}$

3. $\frac{10^6\text{V}}{\text{s}}$

3. $\frac{\text{I}}{\text{c}}$

1. In the x direction and in phase with the $\overline{\text{E}}$ field