State two ways in which the intensity pattern on the screen changes.

Calculate the wavelength of the light in water.

In two different experiments, white light is passed through a single slit and then is either refracted through a prism or diffracted with a diffraction grating. The prism produces a band of colours from M to N. The diffraction grating produces a first order spectrum P to Q.

What are the colours observed at M and P?

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

A ray of light is incident on the flat side of a semi-circular glass block placed in paraffin. The ray is totally internally reflected inside the glass block as shown.

The refractive index of glass is $n_1$ and the refractive index of paraffin is $n_2$.

What is correct?

A.  $\sin \theta =\frac{n_1}{n_2}$

B.  $\sin \theta =\frac{n_2}{n_1}$

C.  $\sin \theta =\frac{1}{n_1}$

D.  $\sin \theta =\frac{1}{n_2}$

Monochromatic light of wavelength $\lambda$ is incident on two slits S₁ and S₂. An interference pattern is observed on the screen.

O is equidistant from S₁ and S₂. A bright fringe is observed at O and a dark fringe at X.

There are two dark fringes between O and X. What is the path difference between the light arriving at X from the two slits?

A.  $\frac{\lambda }{2}$

B.  $\frac{3\lambda }{2}$

C.  $\frac{5\lambda }{2}$

D.  $\frac{7\lambda }{2}$

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

In a double-slit experiment, a source of monochromatic red light is incident on slits S₁ and S₂ separated by a distance $d$. A screen is located at distance $x$ from the slits. A pattern with fringe spacing $y$ is observed on the screen.

Three changes are possible for this arrangement

I.    increasing $x$

II.   increasing $d$

III.  using green monochromatic light instead of red.

Which changes will cause a decrease in fringe spacing $y$?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II, and III

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Monochromatic light is used to produce double-slit interference fringes on a screen. The fringe separation on the screen is $y$. The distance from the slits to the screen and the separation of the slits are both doubled, and the light source is unchanged. What is the new fringe separation on the screen?

A. $\frac{y}{4}$

B. $y$

C. $2y$

D. $4y$

Show that no light emerges from side AB.

State the frequency of the wave in air.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

P is the first maximum of intensity on one side of M. The following data are available.

d = 0.12 mm

D = 1.5 m

Distance MP = 7.0 mm

Calculate, in nm, the wavelength λ of the light.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10^–7 m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.

Determine the difference between the speed of light corresponding to these two wavelengths in the core glass.

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Calculate the speed of light inside the ice cube.

The refractive index of glass is $\frac{3}{2}$ and the refractive index of water is $\frac{4}{3}$. What is the critical angle for light travelling from glass to water?

A.  ${\sin }^{-1}\left(\frac{1}{2}\right)$

B.  ${\sin }^{-1}\left(\frac{2}{3}\right)$

C.  ${\sin }^{-1}\left(\frac{3}{4}\right)$

D.  ${\sin }^{-1}\left(\frac{8}{9}\right)$

The refractive index for light travelling from medium X to medium Y is $\frac{4}{3}$. The refractive index for light travelling from medium Y to medium Z is $\frac{3}{5}$. What is the refractive index for light travelling from medium X to medium Z?

A. $\frac{4}{5}$

B. $\frac{15}{12}$

C. $\frac{5}{4}$

D. $\frac{29}{15}$

Wavefronts travel from air to medium Q as shown.

What is the refractive index of Q?

A.  $\frac{\sin 30°}{\sin 45°}$

B.  $\frac{\sin 45°}{\sin 30°}$

C.  $\frac{\sin 45°}{\sin 60°}$

D.  $\frac{\sin 60°}{\sin 45°}$

Determine the wavelength of the wave in air. 

Deduce that a minimum intensity of sound is heard at P.

The frequency of the sound wave in the metal is 250 Hz. Determine the wavelength of the wave in air.

Deduce that a minimum intensity of sound is heard at P.

A glass block has a refractive index in air of n_g. The glass block is placed in two different liquids: liquid X with a refractive index of n_X and liquid Y with a refractive index of n_Y.

In liquid X $\frac{n_{\text{g}}}{n_{\text{X}}}=2$ and in liquid Y $\frac{n_{\text{g}}}{n_{\text{Y}}}=1.5.$ What is $\frac{\text{speed of light in liquid X}}{\text{speed of light in liquid Y}}$?

A.  $\frac{2}{4}$

B.  $\frac{3}{4}$

C.  $\frac{4}{3}$

D.  $3$

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10^–7 m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.