Question

In case of diffraction, if \( a \) is a slit width and \( \lambda \) is the wavelength of the incident light, then the required condition for diffraction to take place is:

• A. \( \frac{a}{\lambda} = 1000 \)
• B. \( \frac{a}{\lambda} \leq 1 \)
• C. \( a \ll \lambda \)
• D. \( a \gg \lambda \)

Hint:

Diffraction is significant when the slit width is comparable to or smaller than the wavelength of light.

Answer 1

The Correct Option is B

Step 1: Understanding Diffraction Condition For diffraction to occur, the slit width \( a \) must be of the same order of magnitude as the wavelength \( \lambda \), i.e.: \[ \frac{a}{\lambda} \leq 1 \] Step 2: Explanation - If \( a \gg \lambda \), no noticeable diffraction occurs.
- If \( a \ll \lambda \), diffraction effects are maximized.
- The practical condition is \( \frac{a}{\lambda} \leq 1 \).

Answer 2

Diffraction occurs when a wave encounters an obstacle or a slit comparable in size to its wavelength, causing the wave to bend around the edges.

Given:
- Slit width, \( a \)
- Wavelength of incident light, \( \lambda \)

For significant diffraction to occur, the slit width must be on the order of the wavelength or smaller.

Therefore, the condition for diffraction is:
\[ \frac{a}{\lambda} \leq 1 \] This means the slit width \( a \) should be less than or approximately equal to the wavelength \( \lambda \) for noticeable diffraction patterns to be observed.

If \( a \) is much larger than \( \lambda \), diffraction effects become negligible.

Hence, the required condition for diffraction to take place is:
\[ \boxed{\frac{a}{\lambda} \leq 1} \]