Question

Consider sunlight incident on a slit of width ${10}^3\dot{\text{A}}$. The image seen through the slit shall (The wavelength of sunlight $\left(\text{visible light}\right)$ varies from $4000\dot{\text{A}}$ to $7000\dot{\text{A}}).$

• A. be a fine sharp slit white in colour at the centre.
• B. a bright slit white in colour at the centre diffusing to zero intensities at the edges.
• C. a bright slit, white in colour at the centre diffusing to regions of different colours.
• D. only be a diffused slit white in colour.

Answer 1

The correct option is A be a fine sharp slit white in colour at the centre.

Here, the width, $b$ of the slit is ${10}^3\dot{\text{A}}$, whereas the wavelength of sunlight $\left(\text{visible light}\right)$ varies from $4000\dot{\text{A}}$ to $7000\dot{\text{A}}$.

$b<\lambda$

Condition for first minimum is given by,
$\sin \theta =\frac{\lambda }{b}$

As $a<\lambda \Rightarrow \sin \theta >1,\text{which is not possible}$,

Therefore, no diffraction occurs. Hence, the image seen through the slit shall be a fine, sharp slit white at the centre.

Hence, the correct option is $\left(A\right)$.