Question 58: Wave Optics

Question

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

Accepted Answer

When a plane wave-front (parallel rays) enters a prism, all parts of the wave-front travel at the same speed through the medium. While the wave-front is tilted due to refraction, it remains flat and parallel, thus remaining a plane wave.
According to Huygens' Principle, every point on a wave-front acts as a source of secondary spherical wavelets. When a plane wave encounters a very small opening (pinhole) comparable to the wavelength of light, it undergoes diffraction. The emerging light spreads out in all directions, forming a spherical wave-front.
Hence, the statement I is true.
When light passes through a slit, the degree of spreading (diffraction) depends on the slit width (d) relative to the wavelength ( $\lambda$ ).
Smaller slit widths lead to greater diffraction and more pronounced curvature. As the slit width increases, the light behaves more like a straight beam, meaning the wave-front becomes flatter.
Curvature is the reciprocal of the radius of the wave-front, i.e., $\propto \frac{1}{\mathrm{r}}$. So, a flatter wave has less curvature. Therefore, increasing the slit width decreases the curvature, it does not increase it.
Hence, the statement II is false.
Since Statement I is true and Statement II is false, so the correct option is (C).

Answer

$$ \left(E_x \hat{i}+E_y \hat{j}\right) \sin (k x-k z-\omega t) $$

Answer

$$ \left(E_x \hat{i}+E_z \hat{k}\right) \sin (k x+k y-\omega t) $$

Answer

$$ \left(E_x \hat{j}+E_y \hat{k}\right) \sin (k y+k z-\omega t) $$

Answer

$$ \left(E_x \hat{i}+E_y \hat{j}+E_z \hat{k}\right) \sin (k x+k y-k z-\omega t) $$

Wave Optics

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

Choose the correct answer: