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What is the shape of the wavefront in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a convex lens when a point source is placed at its focus. (c) The portion of the wavefront of light from a distant star intercepted by the Earth.

Short Answer

Expert verified
(a) Spherical wavefronts; (b) Planar wavefronts; (c) Planar wavefronts.

Step by step solution

01

Understanding Wavefronts

A wavefront is a surface over which an optical wave has a constant phase. We will analyze each situation separately to determine the shape of the wavefronts.
02

Analyzing Light from a Point Source (a)

When light diverges from a point source, the wavefronts are spherical in shape. This is because light spreads out uniformly in all directions from a point, creating concentric spheres.
03

Analyzing Light Through a Convex Lens (b)

When a point source is placed at the focus of a convex lens, the emerging light rays become parallel to each other as they exit the lens. Therefore, the wavefront of emerging light rays is planar or flat. This is due to the lens converging the diverging waves into a parallel, planar form.
04

Analyzing Light from a Distant Star (c)

Light from a distant star travels a vast distance to reach the Earth. By the time it reaches us, the wavefronts appear as large planes or flat surfaces, because they are only a small segment of a much larger sphere with a vast radius.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Spherical Wavefront
Imagine dropping a stone into a smooth pond. As the stone displaces the water, ripples form and travel outward in circles. This is much like a spherical wavefront in the world of optics. When light emerges from a point source, such as a tiny bulb or a spark, the light spreads out evenly in all directions.
Just as those ripples form concentric circles on the water's surface, a spherical wavefront forms concentric spheres of light. These concentric spheres have the same phase, maintaining uniformity as they propagate through space.
This understanding of spherical wavefronts is essential for comprehending how light behaves when it emerges from localized sources, offering insight into concepts like diffraction and interference as well.
Planar Wavefront
Imagine beams of light traveling in perfectly straight lines. This concept comes to life when light transitions through specific conditions, such as passing through a convex lens.
When a light source sits precisely at the focal point of a convex lens, the lens adjusts the diverging light rays so that they emerge parallel on the other side. The shift from diverging rays to parallel light results in a planar wavefront, resembling flat sheets or planes.
Planar wavefronts are crucial in optics because they simplify predictions about light's behavior. They make it easier to design optical devices, like telescopes and microscopes, that need predictable, uniform light behavior. These flat wavefronts facilitate clearer images and are fundamental to understanding how lenses and mirrors manipulate light for various applications.
Optical Wave Phase
The phase of an optical wave is a vital concept which refers to the specific stage in the cycle of the wave at any given point in time. Understanding the optical wave phase is key to unlocking the behavior and interaction of light waves.
When discussing wavefronts, the optical wave phase is crucial because it defines areas of constant phase, like on a spherical or planar wavefront. These phases determine how constructive and destructive interference will occur.
For instance, when light waves from a distant star reach Earth, those portions of the wavefront have traveled for so long and over such vast distances that by the time they arrive, they are essentially planar. At this point, the optical wave phase remains constant across large segments, which is why we can observe clear and stable images of celestial bodies, despite their enormous distance from us.
This concept of the optical wave phase underpins many areas of wave optics, including the study of coherence and the development of lasers and other optical technologies that rely on precise phase alignment.

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Most popular questions from this chapter

In a double-slit experiment the angular width of a fringe is found to be \(0.2^{\circ}\) on a screen placed \(1 \mathrm{~m}\) away. The wavelength of light used is \(600 \mathrm{~nm}\). What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be \(4 / 3\).

Answer the following questions: (a) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? (b) In what way is diffraction from each slit related to the interference pattern in a double-slit experiment? (c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why? (d) Two students are separated by a \(7 \mathrm{~m}\) partition wall in a room \(10 \mathrm{~m}\) high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily. (e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?

For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest: observer moving. and (ii) source moving: observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

In deriving the single slit diffraction pattern. it was stated that the intensity is zero at angles of \(n \lambda / a\). Justify this by suitably dividing the slit to bring out the cancellation.

A parallel beam of light of wavelength \(500 \mathrm{~nm}\) falls on a narrow slit and the resulting diffraction pattern is observed on a screen \(1 \mathrm{~m}\) away. It is observed that the first minimum is at a distance of \(2.5\) \(\mathrm{mm}\) from the centre of the screen. Find the width of the slit.

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