Question

At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer’s eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?

Short answer

1. Ring will become larger
2. Red color appears on the outside edge of the ring.

Step-by-step solution

The given data

Given that at night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings.

The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer’s eye.

Concept and Formula used

The analysis of such patterns shows that the first minimum for the diffraction pattern of a circular aperture of diameter d is located by

$\sin \theta =1.22\frac{\lambda }{d}$(first minimum-circular aperture)

Here, $\theta$ is the angle from the central axis to any point on that circular minimum.

Change on ring size on switching the lamp from blue to red

(a)

If the lamp were switched from blue light to red light, light of a longer wavelength will appear as red has larger wavelength than blue.

From the equation: $\sin \theta =1.22\frac{\lambda }{d}$,

As wavelength $\lambda$is increases, the distanced must also increase.

Hence, on switching the lamp from blue light to red light ring will become larger.

Light appearing on the outside edge of the ring

(b)

From part (a) it is clearthat red light will produce a ring with a greater distance than blue light.

If the person sees both rings, the red ring will be outside of the blue ring.

Hence, red color appears on the outside edge of the ring.