Practice Questions

Define coherent sources of light.

Propose a modification to the single-slit diffraction experiment that would cause the diffraction pattern to spread out more on the screen.

Define a wavefront.

Name the phenomenon that describes the bending of light waves as they pass around the corners of an obstacle or through a narrow aperture.

Propose a reason why diffraction effects are not commonly observed for light in everyday life, whereas they are easily noticeable for sound waves.

Identify the shape of the wavefront for light from a distant star.

Justify why the concept of a 'wavefront' is fundamental to Huygens' principle.

Analyze what happens to the intensity of unpolarised light when it passes through a single polaroid sheet. Justify your answer.

Apply the principle of superposition to determine the path difference condition for destructive interference between waves from two coherent sources.

Examine why two independent sources of light, such as two separate light bulbs, cannot produce a sustained interference pattern.

Analyze the shape of the wavefront emerging from a thin convex lens when a plane wavefront is incident on it. Demonstrate your answer with a simple diagram.

Analyze what happens to the interference pattern in a Young's double-slit experiment if the entire apparatus is immersed in water (refractive index $n_w = 4/3$). How does the fringe width change?

Explain what happens to the speed, wavelength, and frequency of a light wave when it refracts from a rarer medium (like air) to a denser medium (like glass).

Define polarisation of a transverse wave.

Explain why two independent light sources, like two separate sodium lamps, cannot produce a sustained interference pattern.

Summarize the setup of Young's double-slit experiment and explain its fundamental significance in the history of physics.

Monochromatic light of wavelength $600 \text{ nm}$ is incident from air on a glass surface. If the refractive index of glass is $1.5$, recall the relevant formula and determine the wavelength of light inside the glass.

Describe the key difference in the prediction of the speed of light in a denser medium made by Newton's corpuscular theory and Huygens' wave theory.

List the conditions for constructive and destructive interference in terms of the path difference between two coherent waves.

Recall the mathematical expression for Malus's Law.

In a Young's double-slit experiment, the two slits are separated by $0.15 \text{ mm}$ and the screen is placed $1.5 \text{ m}$ away. If light of wavelength $600 \text{ nm}$ is used, calculate the fringe width of the interference pattern.

A beam of light with a wavelength of $590 \text{ nm}$ in a vacuum enters a glass block with a refractive index of $1.5$. Calculate the speed and the wavelength of the light inside the glass block. The speed of light in a vacuum is $c = 3 \times 10^8 \text{ m/s}$.

Explain Huygens' principle for the propagation of a wavefront.

A parallel beam of light of wavelength $500 \text{ nm}$ is incident normally on a single slit of width $0.2 \text{ mm}$. Calculate the angular width of the central maximum of the diffraction pattern.

Contrast the predictions made by Newton's corpuscular model and Huygens' wave model regarding the speed of light when it refracts from a rarer medium to a denser medium.

Design an experiment to demonstrate the transverse nature of light waves, distinguishing it from longitudinal waves like sound. Justify your choice of components and predict the expected observations.

Critique the corpuscular model of light as proposed by Newton in light of Huygens' wave theory's explanation for refraction. Justify why the wave theory's prediction about the speed of light in a denser medium was ultimately accepted.

A student claims that in Young's double-slit experiment (YDSE), if the two slits were illuminated by two independent, identical laser sources instead of a single source and two slits, the interference pattern would be much brighter. Evaluate this claim.

Two polaroids are placed with their pass axes crossed. A third polaroid is placed between them. Propose the orientation of the third polaroid that would allow the maximum intensity of light to be transmitted through the system. Formulate an expression for this maximum intensity in terms of the initial intensity $I_0$ of unpolarised light.

Evaluate the statement: "The central maximum in a single-slit diffraction pattern is twice as wide as the secondary maxima." Justify your answer with the mathematical conditions for minima.

Critique Huygens' original principle regarding the absence of a backwave. Explain why his ad-hoc assumption was considered unsatisfactory and how the issue is resolved by more rigorous wave theories.

Evaluate the key differences between the interference pattern produced by a double slit and the diffraction pattern produced by a single slit. Create a table to compare their features, such as fringe width, intensity distribution, and the number of sources involved.

Demonstrate the law of reflection ($i=r$) by applying Huygens' principle. Use a diagram to illustrate the construction of the reflected wavefront.

Compare the intensity distribution patterns of single-slit diffraction and double-slit interference. Mention two key differences.

Unpolarised light of intensity $I_0$ is incident on a polaroid $P_1$. A second polaroid $P_2$ is placed such that its pass axis makes an angle of $60^\circ$ with the pass axis of $P_1$. A third polaroid $P_3$ is placed with its pass axis perpendicular to that of $P_1$. Calculate the intensity of light emerging from $P_3$.

Summarize how Huygens' principle is used to derive the law of reflection for a plane wave incident on a plane surface.

In a Young's double-slit experiment, the distance between the central bright fringe and the fifth bright fringe is measured to be $1.5 \text{ cm}$. The screen is located $1.2 \text{ m}$ from the slits, which are separated by $0.24 \text{ mm}$. Solve for the wavelength of the light used.

A beam of light consisting of two wavelengths, $650 \text{ nm}$ and $520 \text{ nm}$, is used in a Young's double-slit experiment. The distance between the slits is $0.5 \text{ mm}$ and the screen is $1.3 \text{ m}$ away. Solve for the least distance from the central maximum where the bright fringes due to both wavelengths coincide.

Formulate a mathematical proof for the law of reflection ($i=r$) using Huygens' principle. Create a detailed diagram to support your derivation and justify each step in the geometrical construction.

Describe the diffraction pattern produced by a single slit illuminated by monochromatic light and list the condition for the angular positions of the dark fringes (minima).

Design an experiment using a spectrometer and a diffraction grating to determine the wavelengths of the different colours present in a composite light source. Formulate the grating equation and explain how you would use it to calculate the wavelengths from your measurements. Justify why a grating is preferred over a prism for accurate wavelength measurement.

Design a modified Young's double-slit experiment to determine the refractive index of a thin, transparent sheet. Formulate the necessary equations to calculate the refractive index from the observed fringe shift. Justify the placement of the sheet.

In a Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is $I_0$. Solve for the intensity at a point where the path difference is $\lambda/4$.

In a Young's double-slit experiment, a beam of light consisting of two wavelengths, $\lambda_1 = 600 \text{ nm}$ and $\lambda_2 = 480 \text{ nm}$, is used. The slit separation is $d = 0.3 \text{ mm}$ and the screen is placed at a distance $D = 1.5 \text{ m}$ from the slits. Propose a method to find the least distance from the central maximum where the bright fringes due to both wavelengths coincide. Formulate the conditions and calculate this distance.

In a Young's double-slit experiment, the setup is immersed in a liquid of refractive index $n$. Formulate expressions for the new fringe width and the positions of bright fringes. Evaluate the effect of the liquid on the interference pattern compared to when the experiment is conducted in air ($n_{air} \approx 1$). Justify your conclusions.