Superposition

State the principle of superposition.

Calculate $D$.

$D$ = ______ $\text{m}$

The slit separation is now gradually decreased from $0.16\text{ mm}$ to $0.04\text{ mm}$. The distance between the centres of adjacent dark fringes is $x$.

On Fig. 4.3, sketch the variation of $x$ with slit separation.

State what is meant by diffraction of a wave.

Show that the angle $\theta$ at which the first-order bright fringe is formed is $6.2^\circ$.

Determine the value of $\theta$ at which the second-order bright fringe is formed.

$\theta$ = ______ $^\circ$

On Fig. 4.2, sketch the variation of the intensity $I$ with $\theta$ for values of $\theta$ from $-15^\circ$ to $+15^\circ$.

A polarising filter is placed in the path of the light beam that is incident on the diffraction grating in Fig. 4.1. The transmission axis of the filter is at $45^\circ$ to the vertical.

Suggest how the variation of intensity with $\theta$ for the light on the screen compares with the answer in (b)(iii).

Explain how the pattern of bright and dark fringes is formed.

Calculate the frequency of the light emitted by the laser.

frequency = ______ $\text{Hz}$

The double slit is removed. A second laser is placed beside the first laser. The second laser produces visible light of a different frequency from that of the first laser. The beams of light from the two lasers overlap on the screen.

Explain why a steady pattern of bright and dark fringes is not formed on the screen.

Explain how the pattern of bright and dark interference fringes is formed.

The distance between the centres of bright fringe X and bright fringe Y in the pattern is $10.2\ \text{mm}$. The slit spacing is $1.2\ \text{mm}$. The distance from the slits to the screen is $3.1\ \text{m}$.

Calculate the wavelength of the light incident on the slits.

wavelength = ______ $\text{m}$

The light is replaced by different visible light with a shorter wavelength.

State how the new fringe separation will compare to the original fringe separation.

On Fig. 6.2, draw a cross (×) to show the position of a node.

State the phase difference between P and Q.

phase difference = ______ $^{\circ}$

State the phase difference between P and R.

phase difference = ______ $^{\circ}$

Explain how a stationary wave is formed between the vibration generator and the wall.

Calculate the wavelength of the stationary wave shown in Fig. 5.2.

$\text{wavelength}$ = ______ $\text{m}$

Fig. 5.3 shows the stationary wave at time $t = 0$ when all points on the wave are at their maximum displacements.

The period of the wave is $0.16\text{ s}$.

On Fig. 5.3, sketch the shape of the stationary wave at time $t = 0.24\text{ s}$.

Points R and T on the string are a horizontal distance of $0.30\text{ m}$ apart and in the positions shown in Fig. 5.4.

State the phase difference between the oscillations of points R and T.

$\text{phase difference}$ = ______ $^\circ$

Calculate the speed of the progressive waves on the stretched string.

$\text{speed}$ = ______ $\text{m s}^{-1}$

State the principle of superposition.

Coherent light is incident normally on two identical slits X and Y. The diffracted light emerging
from the slits superposes to produce an interference pattern on a screen positioned at a
distance of $1.9\ \text{m}$ from the slits.

Fig. 4.1 shows the arrangement and the central part of the interference pattern of bright and
dark fringes formed on the screen.

The separation of the slits is $0.65\ \text{mm}$. The distance between the centres of adjacent bright
fringes is $1.7\ \text{mm}$.

Calculate the wavelength $\lambda$ of the light.

$\lambda$ = ______ $\text{m}$

Explain how statement 1 is correct.

State and explain whether statement 2 is correct.

The width of each slit in (b) is decreased by the same amount. There is no change to the
separation of the slits.

Describe and explain the effect, if any, of this change on the appearance of the interference
pattern.

Explain how the stationary wave is formed on the string.

On Fig. 5.1, sketch a line to show a possible position of the string a quarter of a cycle later than the position shown in the diagram.

Determine the horizontal distance from A to B.

distance = ______ $\text{m}$

A particle on the string has zero displacement at time $t = 0$. From time $t = 0$ to time $t = 0.060\text{ s}$, the particle moves through a total distance of $72\text{ mm}$.

Calculate the amplitude of oscillation of the particle.

amplitude = ______ $\text{mm}$

The light waves from the two slits are coherent.

State what is meant by coherent.

the difference in their path lengths, in nm, from the slits

path difference = ______ $\text{nm}$

their phase difference.

phase difference = ______ $^\circ$

Calculate the distance OQ.

distance OQ = ______ $\text{m}$

The intensity of the light incident on the double slit is increased without changing the frequency.

Describe how the appearance of the fringes after this change is different from, and similar to, their appearance before the change.

The light of wavelength $660\ \text{nm}$ is now replaced by blue light from a laser.

State and explain the change, if any, that must be made to the separation of the two slits so that the fringe separation on the screen is the same as it was for light of wavelength $660\ \text{nm}$.

State the principle of superposition.

Two waves, with intensities $I$ and $4I$, superpose. The waves have the same frequency.

Determine, in terms of $I$, the maximum possible intensity of the resulting wave.

maximum intensity = ______ $I$

Determine the distance between the centres of adjacent bright fringes on the screen.

distance = ______ $\text{m}$

The light of wavelength $550\ \text{nm}$ is replaced with red light of a single frequency.

State and explain the change, if any, in the distance between the centres of adjacent bright fringes.

Describe a simple way that a student, without requiring any additional equipment, can detect when a stationary wave is formed in the air column as the tube is being raised.

Determine the height of the top end of the tube above the surface of the water when a stationary wave is first produced in the tube. Assume that an antinode is formed level with the top of the tube.

height = ______ $\text{m}$

Determine the distance moved by the tube between the positions at which the first and second stationary waves were formed.

distance = ______ $\text{m}$