Question 59: Wave Optics

Question

Given below are two statements :
Statement I :
A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement II :
The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below :

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

Both Statement I and Statement II are false

Answer

Both Statement I and Statement II are true

Answer

Statement I is true but Statement II is false

Answer

Statement I is false but Statement II is true

Wave Optics

Choose the correct answer: