Question

Consider sunlight incident on a pinhole of width ${10}^4\dot{\text{A}}$. The image of the Pinhole seen on a screen shall be (the wavelength of sunlight ranges from $4000\dot{\text{A}}$ to $7000\dot{\text{A}}$

• A. a sharp white ring
• B. different from a geometrical image
  
• C. a diffused white central spot
• D. a diffused coloured region around a sharp central white spot

Answer 1

Answer: (B), (D)

a diffused coloured region around a sharp central white spot

As the width of a pinhole is ${10}^4\dot{\text{A}}=10000\dot{\text{A}}$ and the wavelength of sunlight ranges from $4000\dot{\text{A}}$ to $7000\dot{\text{A}}$,

$\text{Width of the slit}\left(b\right)>\text{wavelength of light}\left(\lambda \right)$

And also $b$ is comparable to $\lambda$,

Therefore, sunlight is diffracted on passing through the pinhole.

Due to diffraction of sunlight on passing through the pinhole, the central spot, which is white, will be of larger width than the pinhole.

So, the image of the pinhole seen on the screen shall be different from a geometrical image.

$\therefore$ Option $\left(B\right)$ is correct.

And also, in diffraction,
As fringe width $\beta \propto \lambda$ and ${\lambda }_{red}>{\lambda }_{violet}$

So, the fringe width of violet light will be smallest.

Due to this, the image of the pinhole will consist of a diffused coloured region around a sharp central white spot

$\therefore$ Option $\left(D\right)$ is also correct.

Hence, correct options are $\left(B\right)$ and $\left(D\right)$.