Chapter 36, Problem 1PQ

Many circular apertures are adjustable, such as the pupil of your eye or the shutter of a camera. Describe the change in the diffraction pattern as such an aperture decreases in size.

To determine

The reason of change in the diffraction pattern in case size of aperture decreases.

Answer to Problem 1PQ

Increase in the aperture size makes the central maximum smaller and decrease in the aperture size makes the central maximum larger.

Explanation of Solution

The diffraction pattern is generated when light pass through the circular aperture and form central bright spot and on both sides consecutive dark bright rings.

Write the equation of the angular radius of the central bright ring.

${\theta }_{\text{R}}=\frac{1.22\lambda }{d}$

Here, $\lambda$ is the wavelength of the light used and $d$ is the diameter of the aperture and angular radius of the central bright ring is ${\theta }_{\text{R}}$.

From the above equation, we can say that angular radius of the central ring is directly proportional to the wavelength of the light used and inversely proportional to the diameter aperture.

Conclusion:

Therefore, increase in the aperture size makes the central maximum smaller and decrease in the aperture size makes the central maximum larger.