Reflection of a Plane Wave by a Plane Surface

A plane wave AB is incident at an angle i on a reflecting surface MN. If v is the speed of the wave in the medium and τ is the time taken by the wavefront to advance from point B to C, then:

To construct the reflected wavefront, a sphere of radius vτ is drawn from point A. From point C, a tangent plane CE is drawn to this sphere. Then:

AB and CE represent the incident and reflected wavefronts, respectively. Considering triangles EAC and BAC, they are congruent, so the angles i and r are equal. Therefore, this gives the law of reflection.

Once the laws of reflection and refraction are known, the behaviour of prisms, lenses, and mirrors can be understood. The source explains only the behaviour of wavefronts as they undergo reflection or refraction.

Plane Wave Through a Thin Prism

• A plane wave passes through a thin prism.
• The speed of light waves is less in glass.
• The lower portion of the incoming wavefront travels through the greatest thickness of glass and gets delayed more.
• This causes a tilt in the emerging wavefront.

Plane Wave Through a Thin Convex Lens

• A plane wave is incident on a thin convex lens.
• The central part of the incident plane wave passes through the thickest portion of the lens and is delayed the most.
• The emerging wavefront has a depression at the centre.
• Therefore, the wavefront becomes spherical and converges to point F, called the focus.

Plane Wave Reflected by a Concave Mirror

• A plane wave is incident on a concave mirror.
• On reflection, a spherical wave is formed.
• This spherical wave converges to the focal point F.

Similar Understanding

• Similarly, refraction and reflection by concave lenses and convex mirrors can be understood.

From the discussion, the total time taken from a point on the object to the corresponding point on the image is the same when measured along any ray.

For example, when a convex lens focuses light to form a real image:

• The ray going through the centre travels a shorter path.
• But the speed is slower in glass.
• Therefore, the time taken is the same as for rays travelling near the edge of the lens.

Different rays may travel different paths, but the total time from object point to image point remains the same.

Questions

a. When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency. Explain why.

b. When light travels from a rarer to a denser medium, the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave?

c. In the wave picture of light, the intensity of light is determined by the square of the amplitude of the wave. What determines the intensity of light in the photon picture of light?

Solutions

a. Same Frequency of Reflected and Refracted Light

Reflection and refraction arise through the interaction of incident light with the atomic constituents of matter. Atoms may be viewed as oscillators that take up the frequency of an external agency, resulting in forced oscillations. The frequency of light emitted by a charged oscillator equals its frequency of oscillation. Thus, the frequency of scattered light equals that of the incident light.

b. Energy and Speed

No. Energy carried by a wave depends on the amplitude of the wave, not on the speed of wave propagation.

c. Intensity in the Photon Picture

For a given frequency, the intensity of light in the photon picture is determined by the number of photons crossing a unit area per unit time.