Question

The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be

• A. 4
• B. 7
• C. 12
• D. 15

Hint:

In Fraunhofer diffraction, the number of intensity minima is determined by the ratio of slit width to wavelength.

Answer 1

The Correct Option is D

Step 1: Understanding the diffraction pattern.
In the Fraunhofer diffraction pattern for a single slit, intensity minima occur at angles given by the equation: \[ a \sin \theta = m \lambda \] where \(a\) is the slit width, \(\theta\) is the diffraction angle, \(m\) is the order of the minima, and \(\lambda\) is the wavelength of the light. The condition for intensity minima is when \(m\) is an integer (excluding \(m=0\) for the central maximum).

Step 2: Calculating the maximum number of minima.
To calculate the maximum number of minima, we use the formula for the angle of the minima and solve for the highest value of \(m\) where the sine term remains less than or equal to 1: \[ a \sin \theta = m \lambda \quad \text{with} \quad \theta = 90^\circ \quad \Rightarrow \quad a = m \lambda \] Given \(a = 10 \, \mu m\) and \(\lambda = 0.630 \, \mu m\), we find \(m = 7\) as the maximum number of minima.

Step 3: Conclusion.
The correct answer is (B) 7 because there are 7 intensity minima observable in this diffraction pattern.