Question 56: Wave Optics

Question

A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{	ext {st }}$ and $3^{	ext {rd }}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is $\_\_\_\_$ .

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

$$ \frac{D \lambda}{a} $$

Answer

$$ 1.5 \frac{D \lambda}{a} $$

Answer

$$ 2 \frac{D \lambda}{a} $$

Answer

$$ 3 \frac{D \lambda}{a} $$

Wave Optics

A slit of width a is illuminated by light of wavelength \lambda. The linear separation between 1^{\text {st }} and 3^{\text {rd }} minima in the diffraction pattern produced on a screen placed at a distance D from the slit system is \_\_\_\_ .

Choose the correct answer: